Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
514 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 125 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×#407 | C2 |
| socle | C22×C59 | C22×D4 |
| hypercenter | #407 | D59 |
| hypocenter | C59 | #3192 |
| LCS | G ▷ C2×C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ C23×C4 ◁ #407 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14273701 | C2 | semidirect |
| 2. #16837721 | C2 | semidirect |
| 3. #16837655 | C2 | semidirect |
| 4. #16837538 | C2 | semidirect |
| 5. C59×#407 | C2 | semidirect |
| 6. C22×D236 | C22 | semidirect |
| 8. C2×D472 | C22 | semidirect |
| 12. #14273701 | C22 | semidirect |
| 13. C2×C4⋊Dic59 | C22 | semidirect |
| 15. #14273659 | C22 | semidirect |
| 16. #14273649 | C22 | semidirect |
| 18. C2×M16×C59 | C22 | semidirect |
| 19. C22⋊C8×C59 | C22 | semidirect |
| 88. #407 | D59 | semidirect |
| 89. C59 | #3192 | semidirect |
| 94. C2×M16 | C2×D59 | semidirect |
| 103. C22⋊C8 | C2×D59 | semidirect |