Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
232 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 232 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 | C2×C4 | D4×D59 |
| commutator | C4×C59 | C2×C42 |
| Frattini | C22×C4 | C22×D59 |
| Fitting | C59×#339 | C2 |
| socle | C22×C59 | C4×D4 |
| hypercenter | #339 | D59 |
| hypocenter | C59 | #1772 |
| LCS | G ▷ C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C2×C4 ◁ C22×C4 ◁ #339 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 12. #14273662 | C4 | semidirect |
| 13. #14273660 | C4 | semidirect |
| 14. #14273658 | C4 | semidirect |
| 18. C4×C59⋊C8 | C4 | semidirect |
| 87. C59 | #1772 | semidirect |