Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
228 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 59 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | #14273697 |
| commutator | C42×C59 | C23 |
| Frattini | C42 | C22×D59 |
| Fitting | C59×Q8⋊C8 | C2 |
| socle | C22×C59 | #120 |
| hypercenter | Q8⋊C8 | D59 |
| hypocenter | C59 | #1623 |
| LCS | G ▷ C42×C59 ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ Q8⋊C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. Q8×Dic118 | C2 | semidirect |
| 5. #16837150 | C2 | semidirect |
| 6. #16837134 | C2 | semidirect |
| 7. C59×Q8⋊C8 | C2 | semidirect |
| 52. Q8×C59 | SD16 | semidirect |
| 69. Dic118 | SD16 | semidirect |
| 98. Q8⋊C8 | D59 | semidirect |
| 99. C59 | #1623 | semidirect |
| 148. Q8 | #11745660 | semidirect |