Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
406 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 406 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. #22612198 | C2 | semidirect |
| 2. #22611966 | C2 | semidirect |
| 3. #22609410 | C2 | semidirect |
| 4. #22607974 | C2 | semidirect |
| 5. #22607898 | C2 | semidirect |
| 6. #22607889 | C2 | semidirect |
| 7. C73×#3273 | C2 | semidirect |
| 11. #17988964 | C22 | semidirect |
| 13. C4⋊#11924003 | C22 | semidirect |
| 15. #17988363 | C22 | semidirect |
| 16. #17988338 | C22 | semidirect |
| 98. D8×C73 | D8 | semidirect |
| 180. #3273 | D73 | semidirect |
| 187. C73 | #12324 | semidirect |
| 275. D8 | #11924013 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612198 | 2 |
| #22611966 | 2 |
| #22609410 | 2 |
| #22607974 | 2 |
| #22607898 | 2 |
| #22607889 | 2 |
| C73×#3273 | 2 |
| #12324 | 73 |