Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
3000 conjugacy classes of subgroups; only the 725 normal subgroups are shown.
This group has 3000 conjugacy classes of subgroups — too many to draw. Only its 725 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D59 |
| commutator | C22×C59 | C25 |
| Frattini | C22 | C24×D59 |
| Fitting | C23×D4×C59 | C2 |
| socle | C24×C59 | C23 |
| hypercenter | C23×D4 | D59 |
| hypocenter | C59 | C22×#127 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C24 ◁ C23×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×D236 | C2 | semidirect |
| 2. C23×C22⋊D59 | C2 | semidirect |
| 3. C2×#14273723 | C2 | direct (N × H) |
| 4. C22×C4×Dic59 | C2 | semidirect |
| 5. C23×D4×C59 | C2 | semidirect |
| 8. C22×D236 | C22 | semidirect |
| 10. C22×C22⋊D59 | C22 | semidirect |
| 12. #14273723 | C22 | direct (N × H) |
| 13. C2×C4×Dic59 | C22 | semidirect |
| 16. C22×D4×C59 | C22 | semidirect |
| 26. C2×D4×C59 | C23 | semidirect |
| 27. C22×C4×C59 | D4 | semidirect |
| 30. C2×C22⋊D59 | C23 | semidirect |
| 31. C22×Dic59 | D4 | semidirect |
| 34. C2×D236 | C23 | semidirect |
| 35. C4×Dic59 | C23 | semidirect |
| 48. C2×C4×C59 | C2×D4 | semidirect |
| 51. C2×Dic59 | C2×D4 | semidirect |
| 57. C22×C59 | #127 | semidirect |
| 64. C4×C59 | C22×D4 | semidirect |
| 65. Dic59 | C22×D4 | semidirect |
| 68. C2×C59 | C2×#127 | semidirect |
| 74. C23×D4 | D59 | semidirect |
| 77. C59 | C22×#127 | semidirect |
| 85. C22×D4 | C2×D59 | semidirect |
| 102. C2×D4 | C22×D59 | semidirect |
| 105. C22×C4 | C22⋊D59 | semidirect |
| 124. C2×C4 | C2×C22⋊D59 | semidirect |
| 132. C22 | #14273723 | direct (N × H) |
| 137. C4 | C22×C22⋊D59 | semidirect |
| 140. C2 | C2×#14273723 | direct (N × H) |