Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1016 conjugacy classes of subgroups; only the 224 normal subgroups are shown.
This group has 1016 conjugacy classes of subgroups — too many to draw. Only its 224 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. #22626775 | C2 | semidirect |
| 2. #22626503 | C2 | semidirect |
| 3. #22625402 | C2 | semidirect |
| 4. #22625398 | C2 | semidirect |
| 5. #22625387 | C2 | semidirect |
| 6. #22625383 | C2 | semidirect |
| 180. C73 | #17655 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626775 | 2 |
| #22626503 | 2 |
| #22625402 | 2 |
| #22625398 | 2 |
| #22625387 | 2 |
| #22625383 | 2 |
| #22623938 | 2 |
| #17655 | 73 |