Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1038 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 1038 conjugacy classes of subgroups — too many to draw. Only its 147 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. #22609855 | C2 | semidirect |
| 2. #22608435 | C2 | semidirect |
| 3. #22608202 | C2 | semidirect |
| 11. C2×2−1+4×C73 | C4 | semidirect |
| 16. #536×C73 | C4 | semidirect |
| 19. #519×C73 | C4 | semidirect |
| 172. C73 | #8455 | semidirect |
| 173. C2×2−1+4 | Dic73 | semidirect |
| 178. #536 | Dic73 | semidirect |
| 181. #519 | Dic73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22609855 | 2 |
| #22608435 | 2 |
| #22608202 | 2 |
| C73×#3486 | 2 |
| #8455 | 73 |