Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
1252 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 1252 conjugacy classes of subgroups — too many to draw. Only its 253 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 | C22×C61 | C23×C4 |
| Fitting | C61×#380 | C2 |
| socle | C23×C61 | C24 |
| hypercenter | #380 | D61 |
| hypocenter | C61 | D4×C22⋊C4 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ #380 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#14519739 | C2 | semidirect |
| 3. C2×C22⋊C4×D61 | C2 | semidirect |
| 4. #16839663 | C2 | semidirect |
| 5. #16839640 | C2 | semidirect |
| 6. #16839617 | C2 | semidirect |
| 7. C4×C22⋊Dic61 | C2 | semidirect |
| 8. C61×#380 | C2 | semidirect |
| 11. C22×D244 | C4 | semidirect |
| 15. C22×C4×D61 | C22 | semidirect |
| 19. C2×#11758198 | C22 | semidirect |
| 20. C2×#11758198 | C22 | semidirect |
| 21. C2×#11758198 | C22 | semidirect |
| 23. C2×C4×Dic61 | C22 | semidirect |
| 24. #14519684 | C22 | semidirect |
| 26. C2×C4⋊C4×C61 | C22 | semidirect |
| 28. #95×C61 | C22 | semidirect |
| 34. C23×D61 | C2×C4 | semidirect |
| 38. C22×C4×C61 | C2×C4 | semidirect |
| 48. C2×D244 | C2×C4 | semidirect |
| 49. C2×D244 | C2×C4 | semidirect |
| 57. C22⋊Dic61 | D4 | semidirect |
| 96. C2×Dic61 | C2×D4 | semidirect |
| 99. D244 | C22⋊C4 | semidirect |
| 105. C22×C61 | C4×D4 | semidirect |
| 121. C2×D61 | C2×C22⋊C4 | semidirect |
| 124. C4×C61 | C2×C22⋊C4 | semidirect |
| 141. #380 | D61 | semidirect |
| 144. C61 | D4×C22⋊C4 | semidirect |
| 154. C2×C4⋊C4 | C2×D61 | semidirect |
| 164. #95 | C2×D61 | semidirect |
| 186. C22×C4 | C4×D61 | semidirect |
| 252. C22 | #14519739 | semidirect |
| 262. C4 | C22⋊C4×D61 | semidirect |