Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
452 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 137 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. #16838200 | C2 | semidirect |
| 2. C2×#14273733 | C2 | semidirect |
| 3. #16837674 | C2 | semidirect |
| 4. #16837669 | C2 | semidirect |
| 5. #16837662 | C2 | semidirect |
| 6. C2×#14273663 | C2 | semidirect |
| 7. #16837386 | C2 | semidirect |
| 8. C2×#135×C59 | C2 | semidirect |
| 23. #14273663 | C22 | semidirect |
| 24. #14273663 | C22 | semidirect |
| 25. #14273646 | C22 | semidirect |
| 26. #14273644 | C22 | semidirect |
| 32. C2×Q16×C59 | C22 | semidirect |
| 33. C2×SD16×C59 | C22 | semidirect |
| 34. C2×D8×C59 | C22 | semidirect |
| 134. C2×#135 | D59 | semidirect |
| 141. C59 | #3067 | semidirect |
| 153. C2×Q16 | C2×D59 | semidirect |
| 154. C2×SD16 | C2×D59 | semidirect |
| 155. C2×D8 | C2×D59 | semidirect |