Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
938 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 938 conjugacy classes of subgroups — too many to draw. Only its 171 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. #22620934 | C2 | semidirect |
| 2. #22620480 | C2 | semidirect |
| 3. #22609248 | C2 | semidirect |
| 4. #22608558 | C2 | semidirect |
| 5. #22608529 | C2 | semidirect |
| 8. #17988997 | C22 | semidirect |
| 10. #17988982 | C22 | semidirect |
| 11. #17988946 | C22 | semidirect |
| 18. #17988329 | C22 | semidirect |
| 19. #17988327 | C22 | semidirect |
| 158. C73 | #19006 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620934 | 2 |
| #22620480 | 2 |
| #22609248 | 2 |
| #22608558 | 2 |
| #22608529 | 2 |
| C2×#562×C73 | 2 |
| #19006 | 73 |