Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
348 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 104 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 | C22×#6923 |
| commutator | C22×C61 | C22×C8 |
| Fitting | #95×C61 | C4 |
| socle | C23×C61 | C22×C4 |
| hypercenter | #95 | #6923 |
| hypocenter | C61 | #1850 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ #95 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#14519844 | C2 | semidirect |
| 3. C2×C4⋊#92420 | C2 | semidirect |
| 5. #16840628 | C2 | semidirect |
| 6. #16840628 | C2 | semidirect |
| 52. #11758198 | C8 | semidirect |
| 73. C2×C4×C61 | C2×C8 | semidirect |
| 79. C2×Dic61 | C2×C8 | semidirect |
| 107. C2×D61 | C4⋊C8 | semidirect |
| 133. C61 | #1850 | semidirect |
| 214. C2×C4 | D61⋊C8 | semidirect |