Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
438 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 4. #22608464 | C2 | semidirect |
| 5. #22607840 | C2 | semidirect |
| 6. #22607808 | C2 | semidirect |
| 7. C73×#1472 | C2 | semidirect |
| 10. #17988922 | C4 | semidirect |
| 11. #17988905 | C4 | semidirect |
| 15. #17988743 | C4 | semidirect |
| 16. #17988726 | C4 | semidirect |
| 221. #1472 | D73 | semidirect |
| 224. C73 | #9331 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620761 | 2 |
| #22618991 | 2 |
| #22608488 | 2 |
| #22608464 | 2 |
| #22607840 | 2 |
| #22607808 | 2 |
| C73×#1472 | 2 |
| #9331 | 73 |