Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
400 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D61 |
| commutator | C22×C61 | C22×C8 |
| Fitting | C2×C22⋊C8×C61 | C2 |
| socle | C23×C61 | C22×C4 |
| hypercenter | C2×C22⋊C8 | D61 |
| hypocenter | C61 | #1797 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C22⋊C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#14519706 | C2 | semidirect |
| 4. #16839516 | C2 | semidirect |
| 31. C22×Dic61 | C8 | semidirect |
| 85. C22×C61 | C4⋊C8 | semidirect |
| 99. Dic61 | C22⋊C8 | semidirect |
| 114. C61 | #1797 | semidirect |
| 194. C22 | #14519706 | semidirect |