Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
532 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 139 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. #22620578 | C2 | semidirect |
| 2. #22612210 | C2 | semidirect |
| 3. #22612172 | C2 | semidirect |
| 4. #22612031 | C2 | semidirect |
| 5. #22612014 | C2 | semidirect |
| 6. #22611807 | C2 | semidirect |
| 7. D16×Dic73 | C2 | semidirect |
| 8. #22611526 | C2 | semidirect |
| 9. C73×#2246 | C2 | semidirect |
| 123. #2246 | D73 | semidirect |
| 130. C73 | #33740 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620578 | 2 |
| #22612210 | 2 |
| #22612172 | 2 |
| #22612031 | 2 |
| #22612014 | 2 |
| #22611807 | 2 |
| D16×Dic73 | 2 |
| #22611526 | 2 |
| C73×#2246 | 2 |
| #33740 | 73 |