Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
544 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 185 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 | #2549 |
| 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. #16837334 | C2 | semidirect |
| 3. #16837323 | C2 | semidirect |
| 4. #16837308 | C2 | semidirect |
| 5. #16837300 | C2 | semidirect |
| 34. C22×C4×C59 | Q8 | semidirect |
| 50. C22⋊C4×C59 | Q8 | semidirect |
| 124. C59 | #2549 | semidirect |
| 159. C22×C4 | Dic118 | semidirect |
| 171. C22⋊C4 | Dic118 | semidirect |