Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
802 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 802 conjugacy classes of subgroups — too many to draw. Only its 104 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. #22625795 | C2 | semidirect |
| 2. #22625446 | C2 | semidirect |
| 3. #22625256 | C2 | semidirect |
| 4. #22625170 | C2 | semidirect |
| 227. C73 | #8397 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625795 | 2 |
| #22625446 | 2 |
| #22625256 | 2 |
| #22625170 | 2 |
| C2×#17989301 | 2 |
| #8397 | 73 |