Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
804 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 804 conjugacy classes of subgroups — too many to draw. Only its 181 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, socle | C23×C61 | C24 |
| Fitting | C2×#95×C61 | C2 |
| hypercenter | C2×#95 | D61 |
| hypocenter | C61 | #2656 |
| LCS | G ▷ C23×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ C2×#95 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14519751 | C2 | semidirect |
| 2. #16839699 | C2 | semidirect |
| 3. #16839672 | C2 | semidirect |
| 4. C2×#95×C61 | C2 | semidirect |
| 15. C22×C4×C61 | D4 | semidirect |
| 56. C2×#95 | D61 | semidirect |
| 57. C61 | #2656 | semidirect |
| 72. C22×C4 | D244 | semidirect |