Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
590 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 590 conjugacy classes of subgroups — too many to draw. Only its 151 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 |
|---|---|---|
| 1. #22620444 | C2 | semidirect |
| 3. #22612178 | C2 | semidirect |
| 4. #22612177 | C2 | semidirect |
| 5. #22612172 | C2 | semidirect |
| 6. #22612166 | C2 | semidirect |
| 7. #22611635 | C2 | semidirect |
| 8. #346×D73 | C2 | semidirect |
| 9. C73×#2244 | C2 | semidirect |
| 154. #2244 | D73 | semidirect |
| 158. C73 | #33701 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620444 | 2 |
| #22620358 | 2 |
| #22612178 | 2 |
| #22612177 | 2 |
| #22612172 | 2 |
| #22612166 | 2 |
| #22611635 | 2 |
| #346×D73 | 2 |
| C73×#2244 | 2 |
| #33701 | 73 |