Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
566 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 167 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. #22618542 | C2 | semidirect |
| 2. #22612143 | C2 | semidirect |
| 3. #22611703 | C2 | semidirect |
| 4. C2×#17988400 | C2 | semidirect |
| 5. #22611552 | C2 | semidirect |
| 10. #17988636 | C22 | semidirect |
| 13. #17988409 | C22 | semidirect |
| 15. #17988369 | C22 | semidirect |
| 137. C73 | #33657 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618542 | 2 |
| #22612143 | 2 |
| #22611703 | 2 |
| C2×#17988400 | 2 |
| #22611552 | 2 |
| C73×#3058 | 2 |
| #33657 | 73 |