Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
478 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 81 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. #22619966 | C2 | semidirect |
| 3. #22608569 | C2 | semidirect |
| 5. #22608274 | C2 | semidirect |
| 6. #22607794 | C2 | semidirect |
| 196. C73 | #10041 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620049 | 2 |
| #22619966 | 2 |
| #22608569 | 2 |
| #22608400 | 2 |
| #22608274 | 2 |
| #22607794 | 2 |
| C73×#3216 | 2 |
| #10041 | 73 |