Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
374 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 2. #22625855 | C2 | semidirect |
| 3. #22625509 | C2 | semidirect |
| 5. #22624817 | C2 | semidirect |
| 6. #22624763 | C2 | semidirect |
| 174. C73 | #8900 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626861 | 2 |
| #22625855 | 2 |
| #22625509 | 2 |
| #22625269 | 2 |
| #22624817 | 2 |
| #22624763 | 2 |
| #22608312 | 2 |
| #8900 | 73 |