Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
422 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 3. #22608444 | C2 | semidirect |
| 5. #22608403 | C2 | semidirect |
| 6. #22607759 | C2 | semidirect |
| 7. C73×#1287 | C2 | semidirect |
| 10. #17988992 | C4 | semidirect |
| 11. #17988985 | C4 | semidirect |
| 12. #17988934 | C4 | semidirect |
| 13. #17988934 | C4 | semidirect |
| 174. #1287 | D73 | semidirect |
| 176. C73 | #9279 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22621069 | 2 |
| #22619009 | 2 |
| #22608444 | 2 |
| #22608440 | 2 |
| #22608403 | 2 |
| #22607759 | 2 |
| C73×#1287 | 2 |
| #9279 | 73 |