Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
460 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 24. C2×Q32×C71 | C4 | semidirect |
| 162. C71 | #13020 | semidirect |
| 168. C2×Q32 | Dic71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597208 | 2 |
| C2×#17985815 | 2 |
| #22590060 | 2 |
| #22589256 | 2 |
| #22586436 | 2 |
| #22586428 | 2 |
| C22×Q32×C71 | 2 |
| #13020 | 71 |