Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1386 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 1386 conjugacy classes of subgroups — too many to draw. Only its 216 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 |
|---|---|---|
| 1. #22626611 | C2 | semidirect |
| 2. #22626075 | C2 | semidirect |
| 3. #22626073 | C2 | semidirect |
| 4. #22625768 | C2 | semidirect |
| 5. #22625763 | C2 | semidirect |
| 8. #17989590 | C22 | semidirect |
| 9. C2×#14556652 | C22 | semidirect |
| 11. C2×#14556651 | C22 | semidirect |
| 13. C4×#11924037 | C22 | semidirect |
| 225. C73 | #21801 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626611 | 2 |
| #22626075 | 2 |
| #22626073 | 2 |
| #22625768 | 2 |
| #22625763 | 2 |
| C2×#17989152 | 2 |
| #21801 | 73 |