Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
494 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 139 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16838056 | C2 | semidirect |
| 2. D4×D236 | C2 | semidirect |
| 3. #16837749 | C2 | semidirect |
| 4. #16837716 | C2 | semidirect |
| 5. #16837683 | C2 | semidirect |
| 6. #16837638 | C2 | semidirect |
| 7. #16837598 | C2 | semidirect |
| 8. #16837538 | C2 | semidirect |
| 9. C4×D472 | C2 | semidirect |
| 10. C2×#14273649 | C2 | semidirect |
| 11. C8×D4×C59 | C2 | semidirect |
| 16. C2×D472 | C22 | semidirect |
| 17. #14273727 | C22 | semidirect |
| 23. #14273701 | C22 | semidirect |
| 26. C4×D236 | C22 | semidirect |
| 27. C2×C4⋊Dic59 | C22 | semidirect |
| 28. #14273661 | C22 | semidirect |
| 29. #14273661 | C22 | semidirect |
| 32. #14273649 | C22 | semidirect |
| 33. #14273649 | C22 | semidirect |
| 34. #14273649 | C22 | semidirect |
| 35. #14273649 | C22 | semidirect |
| 36. C22×C8×C59 | C22 | semidirect |
| 38. C4⋊C8×C59 | C22 | semidirect |
| 39. C22⋊C8×C59 | C22 | semidirect |
| 40. C4×C8×C59 | C22 | semidirect |
| 85. D4×C59 | D8 | semidirect |
| 106. D236 | #41 | semidirect |
| 152. C8×D4 | D59 | semidirect |
| 154. C59 | #3294 | semidirect |
| 160. C22×C8 | C2×D59 | semidirect |
| 175. C4⋊C8 | C2×D59 | semidirect |
| 182. C22⋊C8 | C2×D59 | semidirect |
| 183. C4×C8 | C2×D59 | semidirect |
| 240. D4 | D472 | semidirect |