Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
320 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 56 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. #22626228 | C2 | semidirect |
| 2. #22626215 | C2 | semidirect |
| 3. #22625078 | C2 | semidirect |
| 4. #22625059 | C2 | semidirect |
| 12. #17989192 | C4 | semidirect |
| 15. #17988960 | C4 | semidirect |
| 16. #17988956 | C4 | semidirect |
| 22. #433×C73 | C4 | semidirect |
| 154. C73 | #13606 | semidirect |
| 165. #433 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626228 | 2 |
| #22626215 | 2 |
| #22625078 | 2 |
| #22625059 | 2 |
| #22620994 | 2 |
| #13606 | 73 |