Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
678 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 678 conjugacy classes of subgroups — too many to draw. Only its 105 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. #22599647 | C2 | semidirect |
| 2. #22598790 | C2 | semidirect |
| 3. #22589268 | C2 | semidirect |
| 4. #22589260 | C2 | semidirect |
| 5. #22586836 | C2 | semidirect |
| 6. #22586189 | C2 | semidirect |
| 7. C71×#3205 | C2 | semidirect |
| 92. #11765849 | D8 | semidirect |
| 222. #3205 | D71 | semidirect |
| 228. C71 | #10192 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599647 | 2 |
| #22598790 | 2 |
| #22589268 | 2 |
| #22589260 | 2 |
| #22586836 | 2 |
| #22586189 | 2 |
| C71×#3205 | 2 |
| #10192 | 71 |