Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
466 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 90 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. #22626900 | C2 | semidirect |
| 2. #22626246 | C2 | semidirect |
| 3. #22625816 | C2 | semidirect |
| 4. #22624995 | C2 | semidirect |
| 31. #14556664 | D4 | semidirect |
| 182. C73 | #13076 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626900 | 2 |
| #22626246 | 2 |
| #22625816 | 2 |
| #22624995 | 2 |
| #22619591 | 2 |
| #13076 | 73 |