Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
316 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 34. #14556068 | Q8 | semidirect |
| 50. M32×C71 | Q8 | semidirect |
| 133. C71 | #13270 | semidirect |
| 167. M32 | Dic142 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597272 | 2 |
| #22590105 | 2 |
| #22589944 | 2 |
| #22586426 | 2 |
| #22586421 | 2 |
| C71×#1378 | 2 |
| #13270 | 71 |