Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
724 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 724 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 2. C2×#89340 | C2 | semidirect |
| 3. #11729373 | C2 | semidirect |
| 4. C4×#6408 | C2 | semidirect |
| 5. C2×C7×#127 | C4 | semidirect |
| 12. C7×#390 | C4 | semidirect |
| 13. C4×C7×C4⋊C4 | C4 | semidirect |
| 53. #6408 | D4 | semidirect |
| 112. C2×#127 | Dic7 | semidirect |
| 121. #390 | Dic7 | semidirect |
| 123. C4×C4⋊C4 | Dic7 | semidirect |
| 245. C4×C7 | #353 | semidirect |
| 362. C7 | #13223 | semidirect |
| 395. C4 | #89340 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2541 | 2 |
| C2×#89340 | 2 |
| #11729373 | 2 |
| C4×#6408 | 2 |
| #13223 | 7 |