Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
504 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22618987 | C2 | semidirect |
| 3. C2×#17988320 | C2 | semidirect |
| 4. #22608292 | C2 | semidirect |
| 5. #22607818 | C2 | semidirect |
| 6. #22607774 | C2 | semidirect |
| 7. C73×#1504 | C2 | semidirect |
| 9. #17988920 | C4 | semidirect |
| 11. #17988903 | C4 | semidirect |
| 14. #17988737 | C4 | semidirect |
| 16. #17988720 | C4 | semidirect |
| 248. #1504 | D73 | semidirect |
| 253. C73 | #9264 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620692 | 2 |
| #22618987 | 2 |
| C2×#17988320 | 2 |
| #22608292 | 2 |
| #22607818 | 2 |
| #22607774 | 2 |
| C73×#1504 | 2 |
| #9264 | 73 |