Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
422 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 205 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D59 |
| commutator, socle | C22×C59 | C23×C4 |
| Fitting | C59×#525 | C2 |
| hypercenter | #525 | D59 |
| hypocenter | C59 | #2977 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C2×C4 ◁ #525 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16837474 | C2 | semidirect |
| 2. D4×C59⋊C8 | C2 | semidirect |
| 3. #16837463 | C2 | semidirect |
| 4. #16837369 | C2 | semidirect |
| 5. C2×C22⋊(C59⋊C8) | C2 | semidirect |
| 7. C2×#11745664 | C22 | semidirect |
| 9. C22×C59⋊C8 | C22 | semidirect |
| 10. C4⋊(C59⋊C8) | C22 | semidirect |
| 14. C22⋊(C59⋊C8) | C22 | semidirect |
| 15. #14273638 | C22 | semidirect |
| 16. C4×C59⋊C8 | C22 | semidirect |
| 96. C59 | #2977 | semidirect |