Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
268 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 69 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. #22611968 | C2 | semidirect |
| 2. #22608829 | C2 | semidirect |
| 3. #22607995 | C2 | semidirect |
| 4. #22607977 | C2 | semidirect |
| 73. C8×C73 | SD32 | semidirect |
| 97. C73 | #12492 | semidirect |
| 166. C8 | #14556535 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22611968 | 2 |
| #22608829 | 2 |
| #22607995 | 2 |
| #22607977 | 2 |
| C73×#1712 | 2 |
| #12492 | 73 |