Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
416 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
|---|---|---|
| 3. #22625903 | C2 | semidirect |
| 4. #22625888 | C2 | semidirect |
| 5. #22625030 | C2 | semidirect |
| 6. #22625021 | C2 | semidirect |
| 214. C73 | #12963 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626807 | 2 |
| #22625942 | 2 |
| #22625903 | 2 |
| #22625888 | 2 |
| #22625030 | 2 |
| #22625021 | 2 |
| #22611569 | 2 |
| #12963 | 73 |