Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
504 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 177 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D59 |
| commutator, socle | C23×C59 | C24 |
| Frattini | C23 | C23×D59 |
| Fitting | C4×C4⋊C4×C59 | C2 |
| hypercenter | C4×C4⋊C4 | D59 |
| hypocenter | C59 | #2399 |
| LCS | G ▷ C23×C59 ▷ C59 | |
| UCS | C1 ◁ C22×C4 ◁ C4×C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 46. C42×C59 | Q8 | semidirect |
| 55. C4×Dic59 | Q8 | semidirect |
| 112. C59 | #2399 | semidirect |
| 158. C42 | Dic118 | semidirect |