Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
418 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 90 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. #22625853 | C2 | semidirect |
| 2. #22625481 | C2 | semidirect |
| 4. #22624786 | C2 | semidirect |
| 16. #17988665 | C4 | semidirect |
| 17. #17988664 | C4 | semidirect |
| 19. C8×D292 | C4 | semidirect |
| 24. C8×D4×C73 | C4 | semidirect |
| 171. C73 | #8680 | semidirect |
| 179. C8×D4 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625853 | 2 |
| #22625481 | 2 |
| #22625361 | 2 |
| #22624786 | 2 |
| #22618638 | 2 |
| #8680 | 73 |