Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
520 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 185 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×#424 | C2 |
| hypercenter | #424 | D59 |
| hypocenter | C59 | #2929 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C2×C4 ◁ #424 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14273735 | C2 | semidirect |
| 2. C22×C8×D59 | C2 | semidirect |
| 4. #16837472 | C2 | semidirect |
| 5. #16837467 | C2 | semidirect |
| 6. #16837368 | C2 | semidirect |
| 7. #16837365 | C2 | semidirect |
| 8. #16837358 | C2 | semidirect |
| 9. C59×#424 | C2 | semidirect |
| 14. C2×#11745659 | C22 | semidirect |
| 19. C2×C8×D59 | C22 | semidirect |
| 26. (C2×D59)⋊C8 | C22 | semidirect |
| 27. #14273638 | C22 | semidirect |
| 28. C4×C59⋊C8 | C22 | semidirect |
| 32. C4⋊C8×C59 | C22 | semidirect |
| 58. C2×C59⋊C8 | D4 | semidirect |
| 101. C2×D59 | #131 | semidirect |
| 119. #424 | D59 | semidirect |
| 123. C59 | #2929 | semidirect |
| 142. C4⋊C8 | C2×D59 | semidirect |