Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
872 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 872 conjugacy classes of subgroups — too many to draw. Only its 237 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D59 |
| commutator | C22×C59 | C23×C4 |
| Fitting | C4×C22⋊C4×C59 | C2 |
| socle | C23×C59 | C24 |
| hypercenter | C4×C22⋊C4 | D59 |
| hypocenter | C59 | #2341 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ C4×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C4×Dic118 | C2 | semidirect |
| 3. #16837304 | C2 | semidirect |
| 4. #16837302 | C2 | semidirect |
| 5. #16837262 | C2 | semidirect |
| 6. #16837261 | C2 | semidirect |
| 7. #16837249 | C2 | semidirect |
| 8. C4×C22⋊C4×C59 | C2 | semidirect |
| 10. C2×#11745685 | C4 | semidirect |
| 76. C2×C4×C59 | #41 | semidirect |
| 85. Dic118 | C22⋊C4 | semidirect |
| 122. C4×C22⋊C4 | D59 | semidirect |
| 123. C59 | #2341 | semidirect |
| 199. C2×C4 | #11745685 | semidirect |