Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
532 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 100 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. #22625875 | C2 | semidirect |
| 4. #22625874 | C2 | semidirect |
| 5. #22624774 | C2 | semidirect |
| 6. #22624774 | C2 | semidirect |
| 123. C22⋊Dic73 | M16 | semidirect |
| 144. C22⋊C4×C73 | M16 | semidirect |
| 256. C73 | #8852 | semidirect |
| 387. C22⋊C4 | #11924037 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626782 | 2 |
| #22625904 | 2 |
| #22625875 | 2 |
| #22625874 | 2 |
| #22624774 | 2 |
| #99×Dic73 | 2 |
| #8852 | 73 |