Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
650 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 97 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. #11730857 | C2 | semidirect |
| 3. C7×#1505 | C2 | semidirect |
| 4. #11729572 | C2 | semidirect |
| 5. #11728553 | C2 | semidirect |
| 6. #11725555 | C2 | semidirect |
| 7. #11725421 | C2 | semidirect |
| 14. #89856 | C4 | semidirect |
| 15. #89844 | C4 | semidirect |
| 34. C7×C4⋊Q8 | C2×C4 | semidirect |
| 35. C7×#127 | C2×C4 | semidirect |
| 69. C4⋊(C7⋊C8) | C2×C4 | semidirect |
| 76. #1505 | D7 | semidirect |
| 187. D28 | #104 | semidirect |
| 200. C4⋊Q8 | C4×D7 | semidirect |
| 201. #127 | C4×D7 | semidirect |
| 361. C7 | #9325 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11740745 | 2 |
| #11730857 | 2 |
| C7×#1505 | 2 |
| #11729572 | 2 |
| #11728553 | 2 |
| #11725555 | 2 |
| #11725421 | 2 |
| #9325 | 7 |