Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
380 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | #16837310 |
| commutator | C22×C4×C59 | C23 |
| Frattini | C22×C4 | C22×D59 |
| Fitting | C59×#535 | C2 |
| socle | C2×C59 | #392 |
| hypercenter | #535 | D59 |
| hypocenter | C59 | #2008 |
| LCS | G ▷ C22×C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ #535 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16838200 | C2 | semidirect |
| 2. C2×#14273753 | C2 | semidirect |
| 3. #16837419 | C2 | semidirect |
| 4. #16837407 | C2 | semidirect |
| 5. #16837375 | C2 | semidirect |
| 6. #16837172 | C2 | semidirect |
| 7. C59×#535 | C2 | semidirect |
| 53. C2×D236 | D4 | semidirect |
| 55. C2×Dic118 | D4 | semidirect |
| 72. #11745664 | D4 | semidirect |
| 74. C2×C59⋊C8 | D4 | semidirect |
| 145. #535 | D59 | semidirect |
| 150. C59 | #2008 | semidirect |