Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
496 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 131 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D61 |
| commutator | C2×C4×C61 | C24 |
| Frattini | C2×C4 | C23×D61 |
| Fitting | C61×#462 | C2 |
| socle | C22×C61 | C22×D4 |
| hypercenter | #462 | D61 |
| hypocenter | C61 | #3035 |
| LCS | G ▷ C2×C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #462 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14519800 | C2 | semidirect |
| 2. #16840313 | C2 | semidirect |
| 3. C4×#11758226 | C2 | semidirect |
| 4. #16839986 | C2 | semidirect |
| 5. #16839980 | C2 | semidirect |
| 6. #16839964 | C2 | semidirect |
| 7. #16839962 | C2 | semidirect |
| 8. #16839958 | C2 | semidirect |
| 9. C4⋊C8×D61 | C2 | semidirect |
| 10. #16839757 | C2 | semidirect |
| 11. C61×#462 | C2 | semidirect |
| 49. #11758226 | D4 | semidirect |
| 137. C4×C61 | #135 | semidirect |
| 156. #462 | D61 | semidirect |
| 162. C61 | #3035 | semidirect |
| 292. C4 | #14519800 | semidirect |