Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
466 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 101 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×C7×#361 | C2 | semidirect |
| 3. #11729787 | C2 | semidirect |
| 4. #11729204 | C2 | semidirect |
| 5. #11729179 | C2 | semidirect |
| 6. #11728452 | C2 | semidirect |
| 7. #11728444 | C2 | semidirect |
| 14. #89927 | C4 | semidirect |
| 16. #89923 | C4 | semidirect |
| 57. C7×M32 | D4 | semidirect |
| 67. C2×C7⋊C16 | D4 | semidirect |
| 69. C2×#361 | D7 | semidirect |
| 209. M32 | C22⋊D7 | semidirect |
| 325. C7 | #13215 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11741275 | 2 |
| C2×C7×#361 | 2 |
| #11729787 | 2 |
| #11729204 | 2 |
| #11729179 | 2 |
| #11728452 | 2 |
| #11728444 | 2 |
| #13215 | 7 |