Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
412 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 412 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 |
|---|---|---|
| 3. #22625509 | C2 | semidirect |
| 4. #22625508 | C2 | semidirect |
| 5. #22624758 | C2 | semidirect |
| 6. #22624758 | C2 | semidirect |
| 25. #17988335 | C4 | semidirect |
| 26. #17988335 | C4 | semidirect |
| 27. #17988331 | C4 | semidirect |
| 28. #331×C73 | C4 | semidirect |
| 170. C73 | #8935 | semidirect |
| 191. #331 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626812 | 2 |
| #22626065 | 2 |
| #22625509 | 2 |
| #22625508 | 2 |
| #22624758 | 2 |
| #22608590 | 2 |
| #8935 | 73 |