Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1210 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 1210 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. #22619867 | C2 | semidirect |
| 2. #22614218 | C2 | semidirect |
| 3. #22608968 | C2 | semidirect |
| 4. #22608934 | C2 | semidirect |
| 5. #22608460 | C2 | semidirect |
| 6. #22608261 | C2 | semidirect |
| 10. #17988903 | C22 | semidirect |
| 11. #17988898 | C22 | semidirect |
| 15. #17988526 | C22 | semidirect |
| 16. #17988517 | C22 | semidirect |
| 21. #17988321 | C22 | semidirect |
| 22. #17988313 | C22 | semidirect |
| 216. C73 | #18147 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619867 | 2 |
| #22614218 | 2 |
| #22608968 | 2 |
| #22608934 | 2 |
| #22608460 | 2 |
| #22608261 | 2 |
| C2×#537×C73 | 2 |
| #18147 | 73 |