Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
530 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 93 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. #22590984 | C2 | semidirect |
| 3. #22589260 | C2 | semidirect |
| 4. #22586782 | C2 | semidirect |
| 5. #22586233 | C2 | semidirect |
| 6. #22586195 | C2 | semidirect |
| 7. C71×#1505 | C2 | semidirect |
| 10. #17986286 | C4 | semidirect |
| 11. #17986191 | C4 | semidirect |
| 196. #1505 | D71 | semidirect |
| 200. C71 | #9329 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598427 | 2 |
| #22590984 | 2 |
| #22589260 | 2 |
| #22586782 | 2 |
| #22586233 | 2 |
| #22586195 | 2 |
| C71×#1505 | 2 |
| #9329 | 71 |