Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
324 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 63 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. #22611740 | C2 | semidirect |
| 3. #22610078 | C2 | semidirect |
| 4. #22607923 | C2 | semidirect |
| 5. #22607922 | C2 | semidirect |
| 6. #22607915 | C2 | semidirect |
| 7. C73×#1339 | C2 | semidirect |
| 9. #17988984 | C4 | semidirect |
| 10. #17988962 | C4 | semidirect |
| 14. #17988699 | C4 | semidirect |
| 15. #17988698 | C4 | semidirect |
| 155. #1339 | D73 | semidirect |
| 156. C73 | #11837 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620664 | 2 |
| #22611740 | 2 |
| #22610078 | 2 |
| #22607923 | 2 |
| #22607922 | 2 |
| #22607915 | 2 |
| C73×#1339 | 2 |
| #11837 | 73 |