Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
3422 conjugacy classes of subgroups; only the 245 normal subgroups are shown.
This group has 3422 conjugacy classes of subgroups — too many to draw. Only its 245 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×#120×C59 | C2 |
| hypercenter | C2×#120 | D59 |
| hypocenter | C59 | #2846 |
| LCS | G ▷ C23×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ C2×#120 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C25×D59 | C2 | semidirect |
| 2. C2×#14273695 | C2 | semidirect |
| 3. #16837258 | C2 | semidirect |
| 4. #16837257 | C2 | semidirect |
| 5. C2×#120×C59 | C2 | semidirect |
| 9. C22×C22⋊D59 | C22 | semidirect |
| 11. C2×C22⋊Dic59 | C22 | semidirect |
| 12. C2×(C2×D59)⋊C4 | C22 | semidirect |
| 14. C22×D4×C59 | C22 | semidirect |
| 16. C2×C22⋊C4×C59 | C22 | semidirect |
| 18. C24×C59 | D4 | semidirect |
| 20. C24×C59 | C23 | semidirect |
| 26. C23×D59 | D4 | semidirect |
| 30. C22×C4×C59 | C23 | semidirect |
| 32. C22×Dic59 | C23 | semidirect |
| 62. C22×C59 | #120 | semidirect |
| 68. C2×D59 | #120 | semidirect |
| 79. C2×#120 | D59 | semidirect |
| 82. C59 | #2846 | semidirect |
| 88. C22×D4 | C2×D59 | semidirect |
| 93. C2×C22⋊C4 | C2×D59 | semidirect |
| 102. C24 | C22⋊D59 | semidirect |
| 104. C24 | C22×D59 | semidirect |
| 109. C22×C4 | C22×D59 | semidirect |
| 143. C22 | #14273695 | semidirect |