Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
1224 conjugacy classes of subgroups; only the 201 normal subgroups are shown.
This group has 1224 conjugacy classes of subgroups — too many to draw. Only its 201 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 | C2×#121×C59 | C2 |
| hypercenter | C2×#121 | D59 |
| hypocenter | C59 | #2847 |
| LCS | G ▷ C23×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ C2×#121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×C4×D59 | C2 | semidirect |
| 2. C2×#14273698 | C2 | semidirect |
| 3. C2×#14273695 | C2 | semidirect |
| 4. #16837282 | C2 | semidirect |
| 5. #16837278 | C2 | semidirect |
| 6. #16837262 | C2 | semidirect |
| 7. #16837259 | C2 | semidirect |
| 8. C2×#121×C59 | C2 | semidirect |
| 18. C2×C4⋊Dic59 | C22 | semidirect |
| 20. C2×C22⋊Dic59 | C22 | semidirect |
| 22. C59⋊#95 | C22 | semidirect |
| 23. C59⋊#95 | C22 | semidirect |
| 25. C22×D4×C59 | C22 | semidirect |
| 28. C2×C4⋊C4×C59 | C22 | semidirect |
| 29. C2×C22⋊C4×C59 | C22 | semidirect |
| 36. C23×D59 | D4 | semidirect |
| 44. C22×C4×C59 | D4 | semidirect |
| 61. C2×C4×D59 | D4 | semidirect |
| 120. C22×C59 | #121 | semidirect |
| 133. C2×D59 | #121 | semidirect |
| 136. C4×C59 | #120 | semidirect |
| 150. C2×#121 | D59 | semidirect |
| 156. C59 | #2847 | semidirect |
| 160. C22×D4 | C2×D59 | semidirect |
| 171. C2×C4⋊C4 | C2×D59 | semidirect |
| 175. C2×C22⋊C4 | C2×D59 | semidirect |
| 206. C22×C4 | C22⋊D59 | semidirect |
| 276. C22 | #14273698 | semidirect |
| 286. C4 | #14273695 | semidirect |