Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
390 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 69 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. #22621653 | C2 | semidirect |
| 2. #22612186 | C2 | semidirect |
| 3. #22611963 | C2 | semidirect |
| 4. #22607979 | C2 | semidirect |
| 5. #22607891 | C2 | semidirect |
| 6. D4⋊#11924003 | C2 | semidirect |
| 7. C73×#1667 | C2 | semidirect |
| 68. D584 | D8 | semidirect |
| 154. #1667 | D73 | semidirect |
| 158. C73 | #12319 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22621653 | 2 |
| #22612186 | 2 |
| #22611963 | 2 |
| #22607979 | 2 |
| #22607891 | 2 |
| D4⋊#11924003 | 2 |
| C73×#1667 | 2 |
| #12319 | 73 |