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. #22610911 | C2 | semidirect |
| 5. #22608405 | C2 | semidirect |
| 6. #22607825 | C2 | semidirect |
| 7. C73×#1299 | C2 | semidirect |
| 10. #17988996 | C4 | semidirect |
| 11. #17988981 | C4 | semidirect |
| 12. #17988956 | C4 | semidirect |
| 13. #17988947 | C4 | semidirect |
| 205. #1299 | D73 | semidirect |
| 206. C73 | #8998 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620537 | 2 |
| #22619098 | 2 |
| #22610911 | 2 |
| #22608418 | 2 |
| #22608405 | 2 |
| #22607825 | 2 |
| C73×#1299 | 2 |
| #8998 | 73 |