Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1124 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 1124 conjugacy classes of subgroups — too many to draw. Only its 195 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. C23×Dic292 | C2 | semidirect |
| 2. C2×#17989030 | C2 | semidirect |
| 4. #22611867 | C2 | semidirect |
| 5. #22611850 | C2 | semidirect |
| 6. #22611652 | C2 | semidirect |
| 7. C73×#2112 | C2 | semidirect |
| 17. C2×Dic584 | C22 | semidirect |
| 18. C2×#14556536 | C22 | semidirect |
| 24. #17988392 | C22 | semidirect |
| 43. C2×Dic292 | D4 | semidirect |
| 153. C22×C73 | #510 | semidirect |
| 176. #2112 | D73 | semidirect |
| 177. C73 | #33518 | semidirect |
| 325. C22 | #17989030 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic292 | 2 |
| C2×#17989030 | 2 |
| #22619512 | 2 |
| #22611867 | 2 |
| #22611850 | 2 |
| #22611652 | 2 |
| C73×#2112 | 2 |
| #33518 | 73 |