Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
364 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 101 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. #22609786 | C2 | semidirect |
| 3. #22608707 | C2 | semidirect |
| 6. #22607763 | C2 | semidirect |
| 7. C73×#1301 | C2 | semidirect |
| 17. #17988334 | C4 | semidirect |
| 18. #17988330 | C4 | semidirect |
| 161. #1301 | D73 | semidirect |
| 163. C73 | #9581 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22610758 | 2 |
| #22609786 | 2 |
| #22608707 | 2 |
| #22608581 | 2 |
| #22608331 | 2 |
| #22607763 | 2 |
| C73×#1301 | 2 |
| #9581 | 73 |