Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
390 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 83 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. #22588228 | C2 | semidirect |
| 4. #22586350 | C2 | semidirect |
| 5. #22586349 | C2 | semidirect |
| 6. #22586348 | C2 | semidirect |
| 7. C71×#1347 | C2 | semidirect |
| 9. #17986403 | C4 | semidirect |
| 10. #17986374 | C4 | semidirect |
| 14. D8×Dic71 | C4 | semidirect |
| 15. #17986081 | C4 | semidirect |
| 179. #1347 | D71 | semidirect |
| 180. C71 | #11744 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598914 | 2 |
| #22590140 | 2 |
| #22588228 | 2 |
| #22586350 | 2 |
| #22586349 | 2 |
| #22586348 | 2 |
| C71×#1347 | 2 |
| #11744 | 71 |