Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
510 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 83 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. C2×#17988382 | C2 | semidirect |
| 2. C2×#17988327 | C2 | semidirect |
| 3. #22608082 | C2 | direct (N × H) |
| 8. #17988382 | C22 | semidirect |
| 10. #17988327 | C22 | semidirect |
| 11. C2×2−1+4×C73 | C4 | semidirect |
| 16. #454×C73 | C4 | semidirect |
| 19. C2×#101×C73 | C4 | semidirect |
| 29. 2−1+4×C73 | C2×C4 | semidirect |
| 52. #101×C73 | C2×C4 | semidirect |
| 176. C2×C73 | #1404 | semidirect |
| 182. C73 | C2×#1404 | semidirect |
| 183. C2×2−1+4 | Dic73 | semidirect |
| 188. #454 | Dic73 | semidirect |
| 191. C2×#101 | Dic73 | semidirect |
| 201. 2−1+4 | C2×Dic73 | semidirect |
| 226. #101 | C2×Dic73 | semidirect |
| 353. C2 | #22608082 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988382 | 2 |
| C2×#17988327 | 2 |
| #22608082 | 2 |
| C2×#454×C73 | 2 |
| C2×#1404 | 73 |