Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
292 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 105 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×D59 |
| commutator | C22×C59 | C22×C8 |
| Fitting | C59×#336 | C2 |
| socle | C23×C59 | C22×C4 |
| hypercenter | #336 | D59 |
| hypocenter | C59 | #1923 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C22×C4 ◁ #336 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C4⋊(C59⋊C8) | C2 | semidirect |
| 4. C2×C8×Dic59 | C2 | semidirect |
| 6. #16837156 | C2 | semidirect |
| 7. C59×#336 | C2 | semidirect |
| 45. (C2×D59)⋊C4 | C8 | semidirect |
| 129. #336 | D59 | semidirect |
| 130. C59 | #1923 | semidirect |