Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
350 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 57 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. #22599789 | C2 | semidirect |
| 5. #22586357 | C2 | semidirect |
| 6. #22586281 | C2 | semidirect |
| 7. C71×#1350 | C2 | semidirect |
| 166. #1350 | D71 | semidirect |
| 168. C71 | #12165 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599789 | 2 |
| #22590271 | 2 |
| #22590268 | 2 |
| #22589597 | 2 |
| #22586357 | 2 |
| #22586281 | 2 |
| C71×#1350 | 2 |
| #12165 | 71 |