Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
388 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | D4×D59 |
| commutator | C4×C59 | C2×C42 |
| Frattini | C22×C4 | C22×D59 |
| Fitting | C59×#340 | C2 |
| socle | C23×C59 | C2×D4 |
| hypercenter | #340 | D59 |
| hypocenter | C59 | #1762 |
| LCS | G ▷ C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ C22×C4 ◁ #340 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C2×#14273637 | C2 | semidirect |
| 5. C4⋊C4×Dic59 | C2 | semidirect |
| 6. #16837164 | C2 | semidirect |
| 7. C59×#340 | C2 | semidirect |
| 12. #14273689 | C4 | semidirect |
| 17. #14273649 | C4 | semidirect |
| 18. #14273647 | C4 | semidirect |
| 42. C2×C8×C59 | C2×C4 | semidirect |
| 46. C4⋊C4×C59 | C2×C4 | semidirect |
| 49. C4⋊Dic59 | C2×C4 | semidirect |
| 55. C2×C59⋊C8 | C2×C4 | semidirect |
| 88. D236 | C42 | semidirect |
| 130. #340 | D59 | semidirect |
| 131. C59 | #1762 | semidirect |
| 169. C2×C8 | C4×D59 | semidirect |
| 175. C4⋊C4 | C4×D59 | semidirect |