Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1230 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 1230 conjugacy classes of subgroups — too many to draw. Only its 183 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. #22620737 | C2 | semidirect |
| 2. #22615311 | C2 | semidirect |
| 3. #22608934 | C2 | semidirect |
| 4. #22608900 | C2 | semidirect |
| 5. #22608447 | C2 | semidirect |
| 6. #22608261 | C2 | semidirect |
| 10. #17988898 | C22 | semidirect |
| 13. #17988725 | C22 | semidirect |
| 15. #17988517 | C22 | semidirect |
| 16. #17988507 | C22 | semidirect |
| 21. #17988321 | C22 | semidirect |
| 22. #17988313 | C22 | semidirect |
| 221. C73 | #18325 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620737 | 2 |
| #22615311 | 2 |
| #22608934 | 2 |
| #22608900 | 2 |
| #22608447 | 2 |
| #22608261 | 2 |
| C2×#537×C73 | 2 |
| #18325 | 73 |