Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
428 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 76 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. #22626618 | C2 | semidirect |
| 2. #22625401 | C2 | semidirect |
| 3. #22625263 | C2 | semidirect |
| 4. #22625251 | C2 | semidirect |
| 5. #22624824 | C2 | semidirect |
| 6. #22624797 | C2 | semidirect |
| 204. C73 | #9313 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626618 | 2 |
| #22625401 | 2 |
| #22625263 | 2 |
| #22625251 | 2 |
| #22624824 | 2 |
| #22624797 | 2 |
| #22620079 | 2 |
| #9313 | 73 |