Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
352 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 2. #22590140 | C2 | semidirect |
| 3. #22588232 | C2 | semidirect |
| 4. #22586353 | C2 | semidirect |
| 5. #22586351 | C2 | semidirect |
| 9. #17986400 | C4 | semidirect |
| 10. #17986382 | C4 | semidirect |
| 14. #17986093 | C4 | semidirect |
| 16. D8×Dic71 | C4 | semidirect |
| 169. C71 | #11746 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598905 | 2 |
| #22590140 | 2 |
| #22588232 | 2 |
| #22586353 | 2 |
| #22586351 | 2 |
| #22586349 | 2 |
| C71×#1347 | 2 |
| #11746 | 71 |