Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
704 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 237 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 | C4×C4⋊C4×C61 | C2 |
| socle | C23×C61 | C24 |
| hypercenter | C4×C4⋊C4 | D61 |
| hypocenter | C61 | #2349 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ C4×C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #16839660 | C2 | semidirect |
| 4. #16839633 | C2 | semidirect |
| 5. #16839628 | C2 | semidirect |
| 6. #16839621 | C2 | semidirect |
| 7. #95×D61 | C2 | semidirect |
| 8. C4×C4⋊C4×C61 | C2 | semidirect |
| 13. C4×D244 | C4 | semidirect |
| 42. C2×C4×D61 | C2×C4 | semidirect |
| 45. C42×C61 | C2×C4 | semidirect |
| 47. #11758198 | C2×C4 | semidirect |
| 49. C4⋊Dic61 | C2×C4 | semidirect |
| 75. D244 | C4⋊C4 | semidirect |
| 108. C4×C4⋊C4 | D61 | semidirect |
| 110. C61 | #2349 | semidirect |
| 152. C42 | C4×D61 | semidirect |