Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
214 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 214 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 |
|---|---|---|
| 2. #22625043 | C2 | semidirect |
| 3. #22625042 | C2 | semidirect |
| 5. #17989520 | C4 | semidirect |
| 7. #17989518 | C4 | semidirect |
| 75. C73 | #13551 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626352 | 2 |
| #22625043 | 2 |
| #22625042 | 2 |
| #22611526 | 2 |
| #13551 | 73 |