Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
496 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 496 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 |
|---|---|---|
| 3. #22611652 | C2 | semidirect |
| 4. #22610844 | C2 | semidirect |
| 5. #22608028 | C2 | semidirect |
| 6. #22608021 | C2 | semidirect |
| 12. C2×#14556535 | C4 | semidirect |
| 32. C2×Dic292 | C2×C4 | semidirect |
| 42. C2×#11924003 | C2×C4 | semidirect |
| 168. C73 | #13019 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556535 | 2 |
| #22618783 | 2 |
| #22611652 | 2 |
| #22610844 | 2 |
| #22608028 | 2 |
| #22608021 | 2 |
| C2×#361×C73 | 2 |
| #13019 | 73 |