Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
214 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 3. #22624965 | C2 | semidirect |
| 4. #22624964 | C2 | semidirect |
| 5. #22624963 | C2 | semidirect |
| 6. #22624962 | C2 | semidirect |
| 110. C73 | #12035 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625492 | 2 |
| #22625476 | 2 |
| #22624965 | 2 |
| #22624964 | 2 |
| #22624963 | 2 |
| #22624962 | 2 |
| #22611729 | 2 |
| #12035 | 73 |