Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
424 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 91 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. #22618918 | C2 | semidirect |
| 3. #22608477 | C2 | semidirect |
| 4. #22608347 | C2 | semidirect |
| 5. #22607795 | C2 | semidirect |
| 6. #22607793 | C2 | semidirect |
| 7. C73×#1521 | C2 | semidirect |
| 9. #17988982 | C4 | semidirect |
| 10. #17988977 | C4 | semidirect |
| 11. #17988957 | C4 | semidirect |
| 12. #17988953 | C4 | semidirect |
| 207. #1521 | D73 | semidirect |
| 212. C73 | #9370 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620964 | 2 |
| #22618918 | 2 |
| #22608477 | 2 |
| #22608347 | 2 |
| #22607795 | 2 |
| #22607793 | 2 |
| C73×#1521 | 2 |
| #9370 | 73 |