Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
872 conjugacy classes of subgroups; only the 313 normal subgroups are shown.
This group has 872 conjugacy classes of subgroups — too many to draw. Only its 313 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 | C22×#41×C61 | C2 |
| socle | C23×C61 | C24 |
| hypercenter | C22×#41 | D61 |
| hypocenter | C61 | #2341 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ C22×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×Q8×Dic61 | C2 | semidirect |
| 2. #16839665 | C2 | semidirect |
| 3. #16839622 | C2 | semidirect |
| 4. C4×C22⋊Dic61 | C2 | semidirect |
| 14. C2×#41×C61 | C4 | semidirect |
| 40. Q8×C61 | C22⋊C4 | semidirect |
| 52. C2×Dic61 | #41 | semidirect |
| 79. C61 | #2341 | semidirect |
| 81. C2×#41 | Dic61 | semidirect |
| 114. Q8 | C22⋊Dic61 | semidirect |