Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
154 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | #14273698 |
| commutator | C42×C59 | C23 |
| Frattini | C42 | C22×D59 |
| Fitting | C59×#500 | C2 |
| socle | C22×C59 | #121 |
| hypercenter | #500 | D59 |
| hypocenter | C59 | #1695 |
| LCS | G ▷ C42×C59 ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #500 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #16837153 | C2 | semidirect |
| 4. #16837151 | C2 | semidirect |
| 5. C59×#500 | C2 | semidirect |
| 59. #500 | D59 | semidirect |
| 64. C59 | #1695 | semidirect |