Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
438 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22596702 | C2 | semidirect |
| 4. #22586199 | C2 | semidirect |
| 5. #22586198 | C2 | semidirect |
| 6. #22586172 | C2 | semidirect |
| 178. C71 | #10364 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22596702 | 2 |
| #22589169 | 2 |
| #22586900 | 2 |
| #22586199 | 2 |
| #22586198 | 2 |
| #22586172 | 2 |
| C71×#1517 | 2 |
| #10364 | 71 |