Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
584 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D236 |
| commutator | C2×C4×C59 | C24 |
| Frattini | C2×C4 | C23×D59 |
| Fitting | C59×#423 | C2 |
| socle | C22×C59 | C22×D4 |
| hypercenter | #423 | D59 |
| hypocenter | C59 | #3038 |
| LCS | G ▷ C2×C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ #423 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14273755 | C2 | semidirect |
| 2. C2×#14273724 | C2 | semidirect |
| 3. C4×#11745685 | C2 | semidirect |
| 4. #16837603 | C2 | semidirect |
| 5. #16837598 | C2 | semidirect |
| 6. #16837408 | C2 | semidirect |
| 7. C59×#423 | C2 | semidirect |
| 12. C2×#11745660 | C22 | semidirect |
| 13. C2×D472 | C22 | semidirect |
| 17. C4×Dic118 | C22 | semidirect |
| 18. C4×D236 | C22 | semidirect |
| 23. #14273649 | C22 | semidirect |
| 26. C4⋊C8×C59 | C22 | semidirect |
| 32. #11745685 | D4 | semidirect |
| 78. D236 | C2×D4 | semidirect |
| 82. Dic118 | C2×D4 | semidirect |
| 94. C4×C59 | AGL(1,ℤ/8) | semidirect |
| 110. #423 | D59 | semidirect |
| 112. C59 | #3038 | semidirect |
| 130. C4⋊C8 | C2×D59 | semidirect |
| 201. C4 | #14273755 | semidirect |