Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
452 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 177 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D59 |
| commutator, socle | C22×C59 | C23×C4 |
| Fitting | C59×#431 | C2 |
| hypercenter | #431 | D59 |
| hypocenter | C59 | #2975 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C2×C4 ◁ #431 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16837481 | C2 | semidirect |
| 3. #16837479 | C2 | semidirect |
| 4. #16837455 | C2 | semidirect |
| 5. #16837364 | C2 | semidirect |
| 6. C59×#431 | C2 | semidirect |
| 9. C2×#11745659 | C22 | semidirect |
| 16. C4⋊(C59⋊C8) | C22 | semidirect |
| 18. (C2×D59)⋊C8 | C22 | semidirect |
| 19. C4×C59⋊C8 | C22 | semidirect |
| 21. C4⋊C8×C59 | C22 | semidirect |
| 23. C4×C8×C59 | C22 | semidirect |
| 53. C2×C4×C59 | M16 | semidirect |
| 93. #431 | D59 | semidirect |
| 95. C59 | #2975 | semidirect |
| 107. C4⋊C8 | C2×D59 | semidirect |
| 112. C4×C8 | C2×D59 | semidirect |
| 148. C2×C4 | #11745659 | semidirect |