Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
350 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 97 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. C2×#17988365 | C2 | semidirect |
| 4. #22610684 | C2 | semidirect |
| 5. #22608038 | C2 | semidirect |
| 6. #22608029 | C2 | semidirect |
| 14. #17988388 | C4 | semidirect |
| 144. C73 | #13155 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988400 | 2 |
| #22611647 | 2 |
| C2×#17988365 | 2 |
| #22610684 | 2 |
| #22608038 | 2 |
| #22608029 | 2 |
| C73×#1972 | 2 |
| #13155 | 73 |