Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
460 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 159 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 |
|---|---|---|
| 45. Q32×C71 | Q8 | semidirect |
| 87. Dic142 | Q32 | direct (N × H) |
| 114. C71 | Q8×Q32 | semidirect |
| 143. Q32 | Dic142 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×Dic142 | 2 |
| #22590615 | 2 |
| #22590614 | 2 |
| #22590492 | 2 |
| #22590490 | 2 |
| C16×Dic142 | 2 |
| Q32×Dic71 | 2 |
| C4×Q32×C71 | 2 |
| Q8×Q32 | 71 |