Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
1348 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 1348 conjugacy classes of subgroups — too many to draw. Only its 213 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D61 |
| commutator, socle | C23×C61 | C24 |
| Fitting | C23×D4×C61 | C2 |
| hypercenter | C23×D4 | D61 |
| hypocenter | C61 | #2433 |
| LCS | G ▷ C23×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ C23×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14519773 | C2 | semidirect |
| 2. C2×#14519751 | C2 | semidirect |
| 3. C2×#14519746 | C2 | semidirect |
| 4. #16839670 | C2 | semidirect |
| 5. #16839665 | C2 | semidirect |
| 6. C4×C22⋊Dic61 | C2 | semidirect |
| 7. C23×D4×C61 | C2 | semidirect |
| 8. C22×D244 | C22 | semidirect |
| 10. C22×C22⋊D61 | C22 | semidirect |
| 14. C2×C4⋊Dic61 | C22 | semidirect |
| 16. C2×C22⋊Dic61 | C22 | semidirect |
| 17. C2×#11758198 | C22 | semidirect |
| 18. C2×C4×Dic61 | C22 | semidirect |
| 19. #14519684 | C22 | semidirect |
| 38. C2×D4×C61 | D4 | semidirect |
| 40. C22×C4×C61 | D4 | semidirect |
| 53. C22⋊Dic61 | D4 | semidirect |
| 88. C2×Dic61 | C2×D4 | semidirect |
| 99. C22×C61 | #127 | semidirect |
| 109. C4×C61 | #120 | semidirect |
| 120. C23×D4 | D61 | semidirect |
| 127. C61 | #2433 | semidirect |
| 165. C2×D4 | C22⋊D61 | semidirect |
| 169. C22×C4 | C22⋊D61 | semidirect |
| 223. C22 | #14519773 | semidirect |
| 231. C4 | #14519746 | semidirect |