Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
240 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 66 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. #22625564 | C2 | semidirect |
| 2. D8×#10596833 | C2 | semidirect |
| 3. #22624965 | C2 | semidirect |
| 4. #22624885 | C2 | semidirect |
| 5. #22624885 | C2 | semidirect |
| 6. #22624845 | C2 | semidirect |
| 66. D8×C73 | M16 | semidirect |
| 119. C73 | #12073 | semidirect |
| 163. D8 | #11924037 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625564 | 2 |
| D8×#10596833 | 2 |
| #22624965 | 2 |
| #22624885 | 2 |
| #22624845 | 2 |
| D16×Dic73 | 2 |
| #12073 | 73 |