Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
586 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 586 conjugacy classes of subgroups — too many to draw. Only its 99 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. #11741275 | C2 | semidirect |
| 2. C22×#6400 | C2 | semidirect |
| 3. C2×#89680 | C2 | semidirect |
| 4. C2×C7×#361 | C2 | semidirect |
| 5. #11728463 | C2 | semidirect |
| 6. C2×#89292 | C2 | semidirect |
| 7. #11725621 | C2 | semidirect |
| 64. C2×D56 | D4 | semidirect |
| 67. C7×M32 | D4 | semidirect |
| 78. C2×C7⋊C16 | D4 | semidirect |
| 84. C2×#361 | D7 | semidirect |
| 248. M32 | C22⋊D7 | semidirect |
| 385. C7 | #13336 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11741275 | 2 |
| C22×#6400 | 2 |
| C2×#89680 | 2 |
| C2×C7×#361 | 2 |
| #11728463 | 2 |
| C2×#89292 | 2 |
| #11725621 | 2 |
| #13336 | 7 |