Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
422 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 113 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×#17988416 | C2 | semidirect |
| 3. C2×#17988402 | C2 | semidirect |
| 5. #22611528 | C2 | semidirect |
| 6. #22610846 | C2 | semidirect |
| 12. C2×#14556535 | C4 | semidirect |
| 167. C73 | #13246 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556535 | 2 |
| C2×#17988416 | 2 |
| C2×#17988402 | 2 |
| C2×#17988400 | 2 |
| #22611528 | 2 |
| #22610846 | 2 |
| C73×#1978 | 2 |
| #13246 | 73 |