Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
216 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | #14273700 |
| commutator | C2×C4×C59 | C22×C4 |
| Frattini | C22×C4 | C22×D59 |
| Fitting | C59×#344 | C2 |
| socle | C2×C59 | #388 |
| hypercenter | #344 | D59 |
| hypocenter | C59 | #1932 |
| LCS | G ▷ C2×C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #344 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16837450 | C2 | semidirect |
| 5. M16×Dic59 | C2 | semidirect |
| 6. #16837161 | C2 | semidirect |
| 7. C59×#344 | C2 | semidirect |
| 16. #14273645 | C4 | semidirect |
| 17. #14273643 | C4 | semidirect |
| 101. #344 | D59 | semidirect |
| 103. C59 | #1932 | semidirect |