Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
364 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 364 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 |
|---|---|---|
| 2. #22626045 | C2 | semidirect |
| 4. #22625133 | C2 | semidirect |
| 5. #22624828 | C2 | semidirect |
| 6. #22624765 | C2 | semidirect |
| 23. #17988334 | C4 | semidirect |
| 24. #17988332 | C4 | semidirect |
| 25. #17988331 | C4 | semidirect |
| 26. #331×C73 | C4 | semidirect |
| 177. C73 | #9590 | semidirect |
| 192. #331 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626095 | 2 |
| #22626045 | 2 |
| #22625277 | 2 |
| #22625133 | 2 |
| #22624828 | 2 |
| #22624765 | 2 |
| #22608577 | 2 |
| #9590 | 73 |