Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
840 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 189 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 | C59×#380 | C2 |
| hypercenter | #380 | D59 |
| hypocenter | C59 | #2409 |
| LCS | G ▷ C23×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ #380 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×Dic118 | C2 | semidirect |
| 2. C2×#14273707 | C2 | semidirect |
| 4. #16837323 | C2 | semidirect |
| 5. #16837315 | C2 | semidirect |
| 6. #16837307 | C2 | semidirect |
| 8. #16837277 | C2 | semidirect |
| 9. C59×#380 | C2 | semidirect |
| 40. C2×C22⋊D59 | Q8 | semidirect |
| 54. C2×Dic118 | D4 | semidirect |
| 73. C22×D59 | C2×Q8 | semidirect |
| 93. C2×Dic59 | C2×Q8 | semidirect |
| 101. C22×C59 | C22⋊Q8 | semidirect |
| 135. #380 | D59 | semidirect |
| 136. C59 | #2409 | semidirect |
| 233. C22 | #14273707 | semidirect |