Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
456 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 456 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 |
|---|---|---|
| 1. #22626466 | C2 | semidirect |
| 2. #22625414 | C2 | semidirect |
| 4. #22624820 | C2 | semidirect |
| 16. #17988957 | C4 | semidirect |
| 17. #17988956 | C4 | semidirect |
| 18. #17988951 | C4 | semidirect |
| 22. #490×C73 | C4 | semidirect |
| 136. C73 | #9442 | semidirect |
| 142. #490 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626466 | 2 |
| #22625414 | 2 |
| #22625320 | 2 |
| #22624820 | 2 |
| #22620330 | 2 |
| #9442 | 73 |