Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
370 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 141 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. Q8×Dic118 | C2 | semidirect |
| 3. #16837800 | C2 | semidirect |
| 4. #16837799 | C2 | semidirect |
| 7. #16837687 | C2 | semidirect |
| 8. #16837685 | C2 | semidirect |
| 9. C8×Dic118 | C2 | semidirect |
| 51. SD16×C59 | Q8 | semidirect |
| 75. Q8×C59 | C2×Q8 | semidirect |
| 94. Dic118 | SD16 | direct (N × H) |
| 96. C8×C59 | C2×Q8 | semidirect |
| 129. C59 | Q8×SD16 | semidirect |
| 169. SD16 | Dic118 | direct (N × H) |
| 198. Q8 | C2×Dic118 | semidirect |
| 215. C8 | C2×Dic118 | semidirect |