Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
50 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #17989515 | C2 | 1 | 2 | yes | maximal |
| 2 | C32×D73 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #14556662 | — | 2 | 2 | no | — |
| 4 | C16×D73 | C22 | 1 | 1 | yes | characteristic |
| 5 | #14556497 | C4 | 1 | 1 | yes | characteristic |
| 6 | C32×C73 | C4 | 1 | 1 | yes | characteristic |
| 7 | #11924038 | — | 4 | 2 | no | — |
| 8 | C8×D73 | D4 | 1 | 1 | yes | characteristic |
| 9 | #11924003 | Q8 | 1 | 1 | yes | characteristic |
| 10 | C16×C73 | C2×C4 | 1 | 1 | yes | characteristic |
| 11 | C4×D73 | D8 | 1 | 1 | yes | characteristic |
| 12 | #10596833 | — | 8 | 2 | no | — |
| 13 | C8×C73 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 14 | #10596831 | Q16 | 1 | 1 | yes | characteristic |
| 15 | C2×D73 | Q32 | 1 | 1 | yes | characteristic |
| 16 | C4×C73 | #107 | 1 | 1 | yes | characteristic |
| 17 | Dic73 | D16 | 1 | 1 | yes | characteristic |
| 18 | C2×C73 | #366 | 1 | 1 | yes | characteristic |
| 19 | D73 | — | 2 | 1 | no | — |
| 20 | #1425 | — | 73 | 1 | no | maximal, Sylow |
| 21 | C73 | #1425 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 22 | C2×C32 | — | 73 | 1 | no | — |
| 23 | #368 | — | 73 | 2 | no | — |
| 24 | C2×C16 | — | 73 | 1 | no | — |
| 25 | #108 | — | 146 | 2 | no | — |
| 26 | C32 | — | 73 | 1 | no | — |
| 27 | C32 | #64408 | 1 | 1 | yes | characteristic |
| 28 | M16 | — | 292 | 2 | no | — |
| 29 | C2×C8 | — | 73 | 1 | no | — |
| 30 | C16 | — | 73 | 1 | no | — |
| 31 | C16 | C2×#64408 | 1 | 1 | yes | characteristic |
| 32 | C2×C4 | — | 73 | 1 | no | — |
| 33 | C8 | — | 584 | 2 | no | — |
| 34 | C8 | — | 73 | 1 | no | — |
| 35 | C8 | C4⋊#64408 | 1 | 1 | yes | characteristic |
| 36 | C22 | — | 73 | 1 | no | — |
| 37 | C4 | — | 73 | 1 | no | — |
| 38 | C4 | #14556660 | 1 | 1 | yes | characteristic |
| 39 | C2 | — | 146 | 1 | no | — |
| 40 | C2 | #17989513 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #17989513 |
| commutator | C16×C73 | C2×C4 |
| Frattini | C16 | C2×#64408 |
| Fitting | C32×C73 | C4 |
| socle | C2×C73 | #366 |
| hypercenter | C32 | #64408 |
| hypocenter | C73 | #1425 |
| LCS | G ▷ C16×C73 ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ C32 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 21. C73 | #1425 | semidirect |