Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
360 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 178 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C42 | C2×#6923 |
| commutator | C2×C61 | C43 |
| Frattini | C2×C4 | C22×#6923 |
| Fitting | C4×C8×C61 | C4 |
| socle | C22×C61 | C2×C42 |
| hypercenter | C4×C8 | #6923 |
| hypocenter | C61 | C4×#97 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C42 ◁ C4×C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 8. #14519831 | C4 | direct (N × H) |
| 9. C4×#92420 | C4 | semidirect |
| 12. C4×#92418 | C4 | semidirect |
| 13. C8×Dic61 | C4 | semidirect |
| 14. C4×C8×C61 | C4 | semidirect |
| 37. #92420 | C42 | semidirect |
| 38. C8×C61 | C42 | semidirect |
| 39. #92418 | C42 | semidirect |
| 44. C4×C61 | #97 | semidirect |
| 46. Dic61 | #97 | semidirect |
| 56. C61 | C4×#97 | semidirect |
| 66. C4×C8 | #6923 | semidirect |
| 91. C8 | C4×#6923 | semidirect |
| 98. C4 | #14519831 | direct (N × H) |