Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
438 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 72 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. #22626815 | C2 | semidirect |
| 2. #22625455 | C2 | semidirect |
| 3. #22625412 | C2 | semidirect |
| 4. #22625202 | C2 | semidirect |
| 5. #22624838 | C2 | semidirect |
| 6. #22624789 | C2 | semidirect |
| 224. C73 | #9333 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626815 | 2 |
| #22625455 | 2 |
| #22625412 | 2 |
| #22625202 | 2 |
| #22624838 | 2 |
| #22624789 | 2 |
| #22620917 | 2 |
| #9333 | 73 |