Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
414 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 414 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. #22608547 | C2 | semidirect |
| 4. #22608496 | C2 | semidirect |
| 6. #22607813 | C2 | semidirect |
| 7. C73×#1302 | C2 | semidirect |
| 10. #17988996 | C4 | semidirect |
| 11. #17988981 | C4 | semidirect |
| 12. #17988956 | C4 | semidirect |
| 13. #17988947 | C4 | semidirect |
| 204. #1302 | D73 | semidirect |
| 206. C73 | #9431 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620640 | 2 |
| #22618920 | 2 |
| #22608547 | 2 |
| #22608496 | 2 |
| #22608470 | 2 |
| #22607813 | 2 |
| C73×#1302 | 2 |
| #9431 | 73 |