Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
284 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 83 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. #22611747 | C2 | semidirect |
| 2. #22611536 | C2 | semidirect |
| 3. #22607966 | C2 | semidirect |
| 4. #22607964 | C2 | semidirect |
| 134. C73 | #11912 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22611747 | 2 |
| #22611536 | 2 |
| #22607966 | 2 |
| #22607964 | 2 |
| C73×#3174 | 2 |
| #11912 | 73 |