Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
396 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 79 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. #22611473 | C2 | semidirect |
| 3. #22611404 | C2 | semidirect |
| 5. #22607756 | C2 | semidirect |
| 6. #22607753 | C2 | semidirect |
| 195. C73 | #7805 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22617911 | 2 |
| #22611473 | 2 |
| #22611404 | 2 |
| #22611334 | 2 |
| #22607756 | 2 |
| #22607753 | 2 |
| C73×#1270 | 2 |
| #7805 | 73 |