Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
366 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 71 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. #22590576 | C2 | semidirect |
| 2. #22590477 | C2 | semidirect |
| 3. #22587863 | C2 | semidirect |
| 4. #22586383 | C2 | semidirect |
| 5. #22586307 | C2 | semidirect |
| 6. #22586298 | C2 | semidirect |
| 8. #17986404 | C22 | semidirect |
| 11. C4⋊(C71⋊C16) | C22 | semidirect |
| 15. #17985775 | C22 | semidirect |
| 16. #17985750 | C22 | semidirect |
| 172. C71 | #12376 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590576 | 2 |
| #22590477 | 2 |
| #22587863 | 2 |
| #22586383 | 2 |
| #22586307 | 2 |
| #22586298 | 2 |
| C71×#3273 | 2 |
| #12376 | 71 |