Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
668 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 81 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. #22616956 | C2 | semidirect |
| 2. #22611019 | C2 | semidirect |
| 3. #22611002 | C2 | semidirect |
| 4. #22607756 | C2 | semidirect |
| 5. #22607752 | C2 | semidirect |
| 6. #22607751 | C2 | semidirect |
| 7. C73×#2011 | C2 | semidirect |
| 73. C2×Dic146 | D8 | semidirect |
| 265. #2011 | D73 | semidirect |
| 269. C73 | #7742 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22616956 | 2 |
| #22611019 | 2 |
| #22611002 | 2 |
| #22607756 | 2 |
| #22607752 | 2 |
| #22607751 | 2 |
| C73×#2011 | 2 |
| #7742 | 73 |