Finite Group DatabasebetaFinite Group DatabasebetaOrder 8768.
40 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #17984159 | C2 | 1 | 2 | yes | maximal |
| 2 | C16×D137 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #14555520 | — | 2 | 2 | no | — |
| 4 | C8×D137 | C22 | 1 | 1 | yes | characteristic |
| 5 | #14555485 | C4 | 1 | 1 | yes | characteristic |
| 6 | C16×C137 | C4 | 1 | 1 | yes | characteristic |
| 7 | #11764047 | — | 4 | 2 | no | — |
| 8 | C4×D137 | D4 | 1 | 1 | yes | characteristic |
| 9 | #11764040 | Q8 | 1 | 1 | yes | characteristic |
| 10 | C8×C137 | C2×C4 | 1 | 1 | yes | characteristic |
| 11 | C2×D137 | Q16 | 1 | 1 | yes | characteristic |
| 12 | C4×C137 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 13 | Dic137 | D8 | 1 | 1 | yes | characteristic |
| 14 | C2×C137 | #107 | 1 | 1 | yes | characteristic |
| 15 | D137 | — | 2 | 1 | no | — |
| 16 | C137 | #368 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 17 | #368 | — | 137 | 1 | no | maximal, Sylow |
| 18 | C2×C16 | — | 137 | 1 | no | — |
| 19 | #108 | — | 137 | 2 | no | — |
| 20 | M16 | — | 274 | 2 | no | — |
| 21 | C2×C8 | — | 137 | 1 | no | — |
| 22 | C16 | — | 137 | 1 | no | — |
| 23 | C16 | #10587739 | 1 | 1 | yes | characteristic |
| 24 | C2×C4 | — | 137 | 1 | no | — |
| 25 | C8 | — | 548 | 2 | no | — |
| 26 | C8 | — | 137 | 1 | no | — |
| 27 | C8 | C2×#10587739 | 1 | 1 | yes | characteristic |
| 28 | C22 | — | 137 | 1 | no | — |
| 29 | C4 | — | 137 | 1 | no | — |
| 30 | C4 | C4⋊#10587739 | 1 | 1 | yes | characteristic |
| 31 | C2 | — | 274 | 1 | no | — |
| 32 | C2 | #17984157 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 16. C137 | #368 | semidirect |