Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
510 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 112 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. #22625480 | C2 | semidirect |
| 2. #22625232 | C2 | semidirect |
| 3. #22625230 | C2 | semidirect |
| 4. #22625172 | C2 | semidirect |
| 5. #22625171 | C2 | semidirect |
| 6. #22625134 | C2 | semidirect |
| 49. C2×#11924013 | C8 | semidirect |
| 214. C73 | #9668 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625480 | 2 |
| #22625232 | 2 |
| #22625230 | 2 |
| #22625172 | 2 |
| #22625171 | 2 |
| #22625134 | 2 |
| C2×#17988667 | 2 |
| #9668 | 73 |