Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
228 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | #14273696 |
| commutator | C42×C59 | C23 |
| Frattini | C42 | C22×D59 |
| Fitting | D4×Q8×C59 | C2 |
| socle | C22×C59 | #120 |
| hypercenter | D4×Q8 | D59 |
| hypocenter | C59 | #1637 |
| LCS | G ▷ C42×C59 ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ D4×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16837754 | C2 | semidirect |
| 2. #16837697 | C2 | semidirect |
| 4. #16837148 | C2 | semidirect |
| 5. Q8⋊(C59⋊C8) | C2 | semidirect |
| 98. C59 | #1637 | semidirect |