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 |
|---|---|---|
| 2. C2×#17988364 | C2 | semidirect |
| 4. #22610682 | C2 | semidirect |
| 5. #22608037 | C2 | semidirect |
| 6. #22608031 | C2 | semidirect |
| 15. #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 |
|---|---|
| #22611647 | 2 |
| C2×#17988364 | 2 |
| #22610808 | 2 |
| #22610682 | 2 |
| #22608037 | 2 |
| #22608031 | 2 |
| C2×#361×C73 | 2 |
| #13155 | 73 |