Finite Group DatabasebetaFinite Group DatabasebetaOrder 10768.
22 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #19129096 | C2 | 1 | 2 | yes | maximal, direct product factor |
| 2 | C2×#14582089 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C2×D673 | C4 | 1 | 1 | yes | characteristic |
| 4 | #14582089 | C4 | 1 | 1 | yes | characteristic |
| 5 | #14582089 | C22 | 1 | 1 | yes | characteristic |
| 6 | C2×C673 | C8 | 1 | 1 | yes | characteristic, complemented |
| 7 | D673 | C8 | 1 | 1 | yes | characteristic, complemented |
| 8 | D673 | C2×C4 | 1 | 1 | yes | characteristic |
| 9 | C673 | C2×C8 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 10 | C2×C8 | — | 673 | 1 | no | maximal, Sylow |
| 11 | C2×C4 | — | 673 | 1 | no | — |
| 12 | C8 | — | 673 | 2 | no | — |
| 13 | C22 | — | 673 | 1 | no | — |
| 14 | C4 | — | 673 | 1 | no | — |
| 15 | C4 | — | 673 | 1 | no | — |
| 16 | C2 | — | 673 | 1 | no | — |
| 17 | C2 | — | 673 | 1 | no | — |
| 18 | C2 | #19129096 | 1 | 1 | yes | characteristic, direct product factor |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #19129096 |
| commutator, hypocenter | C673 | C2×C8 |
| Frattini | C1 | G |
| Fitting, socle | C2×C673 | C8 |
| prime radical | C2×D673 | C4 |
| cosocle | #14582089 | C22 |
| LCS | G ▷ C673 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #19129096 | C2 | direct (N × H) |
| 6. C2×C673 | C8 | semidirect |
| 7. D673 | C8 | semidirect |
| 9. C673 | C2×C8 | semidirect |
| 18. C2 | #19129096 | direct (N × H) |