Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
900 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 900 conjugacy classes of subgroups — too many to draw. Only its 185 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 | C4×C22⋊C4×C61 | C2 |
| hypercenter | C4×C22⋊C4 | D61 |
| hypocenter | C61 | #2539 |
| LCS | G ▷ C23×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ C4×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14519761 | C2 | semidirect |
| 2. C2×#14519751 | C2 | semidirect |
| 3. C2×#14519747 | C2 | semidirect |
| 4. C22×#11758198 | C2 | semidirect |
| 5. #16839699 | C2 | semidirect |
| 6. #16839672 | C2 | semidirect |
| 7. #16839664 | C2 | semidirect |
| 8. C4×C22⋊C4×C61 | C2 | semidirect |
| 11. C22×D244 | C22 | semidirect |
| 17. C2×C4⋊Dic61 | C22 | semidirect |
| 18. C2×C4⋊Dic61 | C22 | semidirect |
| 23. C2×#11758198 | C22 | semidirect |
| 24. C2×#11758198 | C22 | semidirect |
| 27. C2×C42×C61 | C22 | semidirect |
| 28. #95×C61 | C22 | semidirect |
| 37. C22×C4×C61 | D4 | semidirect |
| 53. C22⋊C4×C61 | D4 | semidirect |
| 137. C4×C22⋊C4 | D61 | semidirect |
| 138. C61 | #2539 | semidirect |
| 157. C2×C42 | C2×D61 | semidirect |
| 158. #95 | C2×D61 | semidirect |
| 179. C22×C4 | D244 | semidirect |
| 190. C22⋊C4 | D244 | semidirect |