Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
422 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 161 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×#433 | C2 |
| hypercenter | #433 | D59 |
| hypocenter | C59 | #2977 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C2×C4 ◁ #433 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16837475 | C2 | semidirect |
| 3. #16837472 | C2 | semidirect |
| 4. C8×D236 | C2 | semidirect |
| 5. #16837467 | C2 | semidirect |
| 6. #16837463 | C2 | semidirect |
| 7. #16837367 | C2 | semidirect |
| 8. C22⋊C8×D59 | C2 | semidirect |
| 9. C59×#433 | C2 | semidirect |
| 12. C2×#11745659 | C22 | semidirect |
| 15. C2×C8×D59 | C22 | semidirect |
| 22. C4⋊(C59⋊C8) | C22 | semidirect |
| 26. (C2×D59)⋊C8 | C22 | semidirect |
| 27. (C2×D59)⋊C8 | C22 | semidirect |
| 28. #14273638 | C22 | semidirect |
| 29. C4×C59⋊C8 | C22 | semidirect |
| 31. C4⋊C8×C59 | C22 | semidirect |
| 33. #97×C59 | C22 | semidirect |
| 34. C4×C8×C59 | C22 | semidirect |
| 121. #433 | D59 | semidirect |
| 124. C59 | #2977 | semidirect |
| 139. C4⋊C8 | C2×D59 | semidirect |
| 147. #97 | C2×D59 | semidirect |
| 149. C4×C8 | C2×D59 | semidirect |