Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
186 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 76 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. #22626355 | C2 | semidirect |
| 2. #22626354 | C2 | semidirect |
| 3. #22625091 | C2 | semidirect |
| 4. #22625049 | C2 | semidirect |
| 5. #22625048 | C2 | semidirect |
| 6. #22625036 | C2 | semidirect |
| 99. C73 | #13647 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626355 | 2 |
| #22626354 | 2 |
| #22625091 | 2 |
| #22625049 | 2 |
| #22625048 | 2 |
| #22625036 | 2 |
| #22611765 | 2 |
| #13647 | 73 |