Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
360 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 209 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C23×D59 |
| commutator, socle | C2×C59 | C23×C8 |
| Fitting | C59×#504 | C2 |
| hypercenter | #504 | D59 |
| hypocenter | C59 | #3407 |
| LCS | G ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C8 ◁ #504 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16837820 | C2 | semidirect |
| 3. #16837819 | C2 | semidirect |
| 4. #16837818 | C2 | semidirect |
| 5. C2×#14273666 | C2 | semidirect |
| 6. M32×D59 | C2 | semidirect |
| 7. C59×#504 | C2 | semidirect |
| 14. #14273667 | C22 | semidirect |
| 17. #14273666 | C22 | semidirect |
| 18. #14273666 | C22 | semidirect |
| 19. C2×C59⋊C16 | C22 | semidirect |
| 20. C16×D59 | C22 | semidirect |
| 22. M32×C59 | C22 | semidirect |
| 23. C2×C16×C59 | C22 | semidirect |
| 77. #504 | D59 | semidirect |
| 80. C59 | #3407 | semidirect |
| 93. M32 | C2×D59 | semidirect |
| 96. C2×C16 | C2×D59 | semidirect |