Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
374 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 133 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. #16838109 | C2 | semidirect |
| 2. D4×Dic118 | C2 | semidirect |
| 3. #16837810 | C2 | semidirect |
| 4. #16837800 | C2 | semidirect |
| 5. #16837704 | C2 | semidirect |
| 6. #16837692 | C2 | semidirect |
| 7. #16837690 | C2 | semidirect |
| 8. #16837682 | C2 | semidirect |
| 9. #16837532 | C2 | semidirect |
| 52. D8×C59 | Q8 | semidirect |
| 78. D4×C59 | C2×Q8 | semidirect |
| 97. C8×C59 | C2×Q8 | semidirect |
| 133. C59 | #3384 | semidirect |
| 174. D8 | Dic118 | semidirect |
| 204. D4 | C2×Dic118 | semidirect |
| 220. C8 | C2×Dic118 | semidirect |