Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
514 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 82 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. #22626502 | C2 | semidirect |
| 2. #22625402 | C2 | semidirect |
| 3. #22625263 | C2 | semidirect |
| 4. #22625252 | C2 | semidirect |
| 5. #22624824 | C2 | semidirect |
| 6. #22624797 | C2 | semidirect |
| 208. C73 | #9311 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626502 | 2 |
| #22625402 | 2 |
| #22625263 | 2 |
| #22625252 | 2 |
| #22624824 | 2 |
| #22624797 | 2 |
| #22620084 | 2 |
| #9311 | 73 |