Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
612 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 170 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×#6923 |
| commutator, socle | C22×C61 | C23×C4 |
| Fitting | #124×C61 | C4 |
| hypercenter | #124 | #6923 |
| hypocenter | C61 | #2326 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ #124 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×Q8×#6923 | C2 | semidirect |
| 3. (C2×#6923)⋊Q8 | C2 | semidirect |
| 5. #16840712 | C2 | semidirect |
| 6. #16840709 | C2 | semidirect |
| 7. #16840708 | C2 | semidirect |
| 8. #16840698 | C2 | semidirect |
| 27. #14519766 | C4 | semidirect |
| 28. #14519765 | C4 | semidirect |
| 29. #14519764 | C4 | semidirect |
| 30. #14519763 | C4 | semidirect |
| 33. #124×C61 | C4 | semidirect |
| 42. C2×Q8×C61 | C2×C4 | semidirect |
| 53. C2×Dic122 | C2×C4 | semidirect |
| 54. C2×Dic122 | C2×C4 | semidirect |
| 64. C22⋊C4×C61 | C2×C4 | semidirect |
| 65. C42×C61 | C2×C4 | semidirect |
| 66. C22⋊Dic61 | C2×C4 | semidirect |
| 67. #11758198 | C2×C4 | semidirect |
| 68. #11758198 | C2×C4 | semidirect |
| 69. C4×Dic61 | C2×C4 | semidirect |
| 70. C4×Dic61 | C2×C4 | semidirect |
| 148. C61 | #2326 | semidirect |
| 156. #124 | #6923 | semidirect |
| 178. C2×Q8 | C2×#6923 | semidirect |
| 203. C22⋊C4 | C2×#6923 | semidirect |
| 209. C42 | C2×#6923 | semidirect |