Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
356 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 356 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 |
|---|---|---|
| 2. #22611727 | C2 | semidirect |
| 3. #22609819 | C2 | semidirect |
| 4. #22607944 | C2 | semidirect |
| 5. #22607942 | C2 | semidirect |
| 9. #17988988 | C4 | semidirect |
| 10. #17988970 | C4 | semidirect |
| 14. #17988681 | C4 | semidirect |
| 16. D8×Dic73 | C4 | semidirect |
| 169. C73 | #11741 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620496 | 2 |
| #22611727 | 2 |
| #22609819 | 2 |
| #22607944 | 2 |
| #22607942 | 2 |
| #22607940 | 2 |
| C73×#1347 | 2 |
| #11741 | 73 |