Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
470 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 109 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. #11739452 | C2 | semidirect |
| 3. #11729204 | C2 | semidirect |
| 4. #11728418 | C2 | semidirect |
| 5. #11728410 | C2 | semidirect |
| 6. C7×#1386 | C2 | semidirect |
| 7. #11725527 | C2 | semidirect |
| 21. #89640 | C4 | semidirect |
| 22. #89637 | C4 | semidirect |
| 54. C7×M32 | D4 | semidirect |
| 63. #6386 | D4 | semidirect |
| 76. #1386 | D7 | semidirect |
| 213. M32 | D28 | semidirect |
| 338. C7 | #13077 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11739452 | 2 |
| #11736565 | 2 |
| #11729204 | 2 |
| #11728418 | 2 |
| #11728410 | 2 |
| C7×#1386 | 2 |
| #11725527 | 2 |
| #13077 | 7 |