Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
414 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 74 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. #22625405 | C2 | semidirect |
| 3. #22625363 | C2 | semidirect |
| 5. #22624825 | C2 | semidirect |
| 6. #22624808 | C2 | semidirect |
| 26. #17988996 | C4 | semidirect |
| 27. #17988955 | C4 | semidirect |
| 28. #17988946 | C4 | semidirect |
| 34. #497×C73 | C4 | semidirect |
| 206. C73 | #9431 | semidirect |
| 210. #497 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626757 | 2 |
| #22625405 | 2 |
| #22625363 | 2 |
| #22625343 | 2 |
| #22624825 | 2 |
| #22624808 | 2 |
| #22620637 | 2 |
| #9431 | 73 |