Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
380 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
|---|---|---|
| 2. #22626287 | C2 | semidirect |
| 4. #22626051 | C2 | semidirect |
| 5. #22624990 | C2 | semidirect |
| 6. #22624987 | C2 | semidirect |
| 25. #17988403 | C4 | semidirect |
| 26. #17988401 | C4 | semidirect |
| 27. #17988399 | C4 | semidirect |
| 28. #362×C73 | C4 | semidirect |
| 169. C73 | #12942 | semidirect |
| 186. #362 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626711 | 2 |
| #22626287 | 2 |
| C2×#17989502 | 2 |
| #22626051 | 2 |
| #22624990 | 2 |
| #22624987 | 2 |
| #22611679 | 2 |
| #12942 | 73 |