Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
836 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 836 conjugacy classes of subgroups — too many to draw. Only its 173 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, socle | C23×C59 | C24 |
| Fitting | C4×C22⋊C4×C59 | C2 |
| hypercenter | C4×C22⋊C4 | D59 |
| hypocenter | C59 | #2432 |
| LCS | G ▷ C23×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×#14273727 | C2 | semidirect |
| 3. C2×#14273715 | C2 | semidirect |
| 4. C2×#14273706 | C2 | semidirect |
| 5. #16837318 | C2 | semidirect |
| 6. #16837308 | C2 | semidirect |
| 7. #16837304 | C2 | semidirect |
| 8. #16837276 | C2 | semidirect |
| 9. C4×C22⋊C4×C59 | C2 | semidirect |
| 93. C2×C4×C59 | #41 | semidirect |
| 145. C4×C22⋊C4 | D59 | semidirect |
| 146. C59 | #2432 | semidirect |
| 241. C2×C4 | #11745685 | semidirect |