Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
396 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 103 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. #22611730 | C2 | semidirect |
| 3. #22607979 | C2 | semidirect |
| 4. #22607976 | C2 | semidirect |
| 5. C73×#1568 | C2 | semidirect |
| 130. #1568 | D73 | semidirect |
| 133. C73 | #11963 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620359 | 2 |
| #22611730 | 2 |
| #22607979 | 2 |
| #22607976 | 2 |
| C73×#1568 | 2 |
| #11963 | 73 |