Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
430 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 96 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. #22626289 | C2 | semidirect |
| 2. #22625488 | C2 | semidirect |
| 3. #22624885 | C2 | semidirect |
| 8. #17989473 | C22 | semidirect |
| 10. #17989450 | C22 | semidirect |
| 75. D8×C73 | M16 | semidirect |
| 135. C73 | #11657 | semidirect |
| 192. D8 | #11924037 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626289 | 2 |
| #22625488 | 2 |
| #22624885 | 2 |
| C2×D8×Dic73 | 2 |
| #11657 | 73 |