Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
652 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 229 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D59 |
| commutator | C22×C59 | C23×C4 |
| Frattini | C23 | C23×D59 |
| Fitting | C43×C59 | C2 |
| socle | C23×C59 | C24 |
| hypercenter | C43 | D59 |
| hypocenter | C59 | #2293 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C22×C4 ◁ C43 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#14273684 | C2 | semidirect |
| 4. #16837300 | C2 | semidirect |
| 5. #16837293 | C2 | semidirect |
| 6. C4×C4⋊Dic59 | C2 | semidirect |
| 7. C4×(C2×D59)⋊C4 | C2 | semidirect |
| 8. C43×C59 | C2 | semidirect |
| 11. C4×D236 | C4 | semidirect |
| 44. C42×C59 | D4 | semidirect |
| 92. C4×C59 | #117 | semidirect |
| 110. C43 | D59 | semidirect |
| 111. C59 | #2293 | semidirect |
| 154. C42 | D236 | semidirect |
| 197. C4 | #14273684 | semidirect |