Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
668 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 668 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. C2×#89687 | C2 | semidirect |
| 2. #11739279 | C2 | semidirect |
| 3. C7×#2249 | C2 | semidirect |
| 4. #11729256 | C2 | semidirect |
| 5. #11729242 | C2 | semidirect |
| 6. #11729222 | C2 | semidirect |
| 7. #11729078 | C2 | semidirect |
| 8. C4×Dic56 | C2 | semidirect |
| 9. #11726809 | C2 | semidirect |
| 74. Dic56 | D4 | semidirect |
| 78. #2249 | D7 | semidirect |
| 308. C7 | #33843 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89687 | 2 |
| #11739279 | 2 |
| C7×#2249 | 2 |
| #11729256 | 2 |
| #11729242 | 2 |
| #11729222 | 2 |
| #11729078 | 2 |
| C4×Dic56 | 2 |
| #11726809 | 2 |
| #33843 | 7 |