Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
402 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 4. #22608092 | C2 | semidirect |
| 5. #22608091 | C2 | semidirect |
| 6. #22608090 | C2 | semidirect |
| 7. C73×#1407 | C2 | semidirect |
| 11. C4⋊Q8×D73 | C4 | semidirect |
| 13. #17988981 | C4 | semidirect |
| 14. #17988979 | C4 | semidirect |
| 19. #17988539 | C4 | semidirect |
| 187. #1407 | D73 | semidirect |
| 188. C73 | #13580 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620387 | 2 |
| #22611613 | 2 |
| #22611595 | 2 |
| #22608092 | 2 |
| #22608091 | 2 |
| #22608090 | 2 |
| C73×#1407 | 2 |
| #13580 | 73 |