Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
952 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 952 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 | C59×#391 | C2 |
| hypercenter | #391 | D59 |
| hypocenter | C59 | #2431 |
| LCS | G ▷ C23×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ #391 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#11745689 | C2 | semidirect |
| 2. C2×#14273724 | C2 | semidirect |
| 3. C2×#14273716 | C2 | semidirect |
| 4. C2×#14273702 | C2 | semidirect |
| 5. #16837312 | C2 | semidirect |
| 6. #16837303 | C2 | semidirect |
| 7. #16837280 | C2 | semidirect |
| 8. C4×(C2×D59)⋊C4 | C2 | semidirect |
| 9. C59×#391 | C2 | semidirect |
| 38. C2×Q8×C59 | D4 | semidirect |
| 59. C2×D236 | D4 | semidirect |
| 65. C2×C4×D59 | D4 | semidirect |
| 100. C2×C4×C59 | #41 | semidirect |
| 154. #391 | D59 | semidirect |
| 158. C59 | #2431 | semidirect |
| 188. C2×Q8 | D236 | semidirect |
| 262. C2×C4 | #11745689 | semidirect |