Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
1460 conjugacy classes of subgroups; only the 754 normal subgroups are shown.
This group has 1460 conjugacy classes of subgroups — too many to draw. Only its 754 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C23×#6923 |
| commutator | C2×C61 | C24×C4 |
| Frattini | C2 | C24×#6923 |
| Fitting | C22×Q8×C61 | C4 |
| socle | C22×C61 | C23×C4 |
| hypercenter | C22×Q8 | #6923 |
| hypocenter | C61 | C2×#568 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ C22×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16840842 | C2 | direct (N × H) |
| 2. C2×#14519865 | C2 | semidirect |
| 3. C2×D61⋊M16 | C2 | semidirect |
| 5. #14519865 | C22 | semidirect |
| 6. C2×#11758213 | C22 | semidirect |
| 7. D61⋊M16 | C22 | semidirect |
| 9. C2×D61⋊C8 | C22 | semidirect |
| 33. #11758213 | C23 | semidirect |
| 34. D61⋊C8 | C23 | semidirect |
| 63. C2×C61 | #568 | semidirect |
| 70. C61 | C2×#568 | semidirect |
| 129. C2 | #16840842 | direct (N × H) |