Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
416 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 10. #17986294 | C4 | semidirect |
| 11. #17986284 | C4 | semidirect |
| 172. C71 | #9308 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598145 | 2 |
| #22597425 | 2 |
| #22586903 | 2 |
| #22586742 | 2 |
| #22586237 | 2 |
| #22586198 | 2 |
| C71×#1805 | 2 |
| #9308 | 71 |