Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
686 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 686 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22612684 | C2 | semidirect |
| 4. #22608463 | C2 | semidirect |
| 5. #22607839 | C2 | semidirect |
| 6. #22607783 | C2 | semidirect |
| 11. #17988743 | C4 | semidirect |
| 12. #17988738 | C4 | semidirect |
| 274. C73 | #9524 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619191 | 2 |
| #22612684 | 2 |
| #22609875 | 2 |
| #22608463 | 2 |
| #22607839 | 2 |
| #22607783 | 2 |
| C73×#1782 | 2 |
| #9524 | 73 |