Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
220 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 64 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 |
|---|---|---|
| 1. #22625570 | C2 | semidirect |
| 3. #22624963 | C2 | semidirect |
| 4. #22624888 | C2 | semidirect |
| 6. #22624842 | C2 | semidirect |
| 61. #11924003 | M16 | semidirect |
| 113. C73 | #12084 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625570 | 2 |
| #22625564 | 2 |
| #22624963 | 2 |
| #22624888 | 2 |
| #22624885 | 2 |
| #22624842 | 2 |
| #22611786 | 2 |
| #12084 | 73 |