Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
438 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 72 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. #22625339 | C2 | semidirect |
| 4. #22625209 | C2 | semidirect |
| 5. #22624835 | C2 | semidirect |
| 6. #22624802 | C2 | semidirect |
| 27. #17988922 | C4 | semidirect |
| 31. #17988745 | C4 | semidirect |
| 32. #17988725 | C4 | semidirect |
| 34. #481×C73 | C4 | semidirect |
| 224. C73 | #9331 | semidirect |
| 229. #481 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626808 | 2 |
| #22625356 | 2 |
| #22625339 | 2 |
| #22625209 | 2 |
| #22624835 | 2 |
| #22624802 | 2 |
| #22620760 | 2 |
| #9331 | 73 |