Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
412 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 3. #22608722 | C2 | semidirect |
| 5. #22607763 | C2 | semidirect |
| 6. #22607763 | C2 | semidirect |
| 7. C73×#1574 | C2 | semidirect |
| 20. #17988335 | C4 | semidirect |
| 21. #17988335 | C4 | semidirect |
| 22. #17988330 | C4 | semidirect |
| 23. #17988330 | C4 | semidirect |
| 166. #1574 | D73 | semidirect |
| 170. C73 | #8935 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618997 | 2 |
| #22610758 | 2 |
| #22608722 | 2 |
| #22608591 | 2 |
| #22607763 | 2 |
| C73×#1574 | 2 |
| #8935 | 73 |