Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1378 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 1378 conjugacy classes of subgroups — too many to draw. Only its 232 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. #22625118 | C2 | semidirect |
| 2. #22625116 | C2 | semidirect |
| 15. #17988524 | C4 | semidirect |
| 16. #17988523 | C4 | semidirect |
| 17. #17988522 | C4 | semidirect |
| 19. #399×C73 | C4 | semidirect |
| 37. C2×C4⋊Dic73 | C2×C4 | semidirect |
| 38. C2×#11924007 | C2×C4 | semidirect |
| 46. #14556498 | C2×C4 | semidirect |
| 47. C2×C4⋊C4×C73 | C2×C4 | semidirect |
| 49. #95×C73 | C2×C4 | semidirect |
| 183. C73 | #14636 | semidirect |
| 192. #399 | #64408 | semidirect |
| 212. C2×C4⋊C4 | C2×#64408 | semidirect |
| 227. #95 | C2×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625118 | 2 |
| #22625116 | 2 |
| #22625114 | 2 |
| #22625104 | 2 |
| #399×D73 | 2 |
| #14636 | 73 |