Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
484 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 484 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 |
|---|---|---|
| 4. #11727332 | C2 | semidirect |
| 5. #11727329 | C2 | semidirect |
| 6. #11725465 | C2 | semidirect |
| 7. #11725465 | C2 | semidirect |
| 25. #89335 | C4 | semidirect |
| 68. #6377 | C2×C4 | semidirect |
| 69. #6377 | C2×C4 | semidirect |
| 368. C7 | #8911 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11740402 | 2 |
| C7×#1959 | 2 |
| C2×#89335 | 2 |
| #11727332 | 2 |
| #11727329 | 2 |
| #11725465 | 2 |
| #8911 | 7 |