Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
586 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 586 conjugacy classes of subgroups — too many to draw. Only its 105 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. C2×#89680 | C2 | semidirect |
| 2. C22×D112 | C2 | semidirect |
| 3. #11736010 | C2 | semidirect |
| 4. C2×#89311 | C2 | semidirect |
| 5. C2×#89305 | C2 | semidirect |
| 6. #11727657 | C2 | semidirect |
| 7. C7×#1379 | C2 | semidirect |
| 59. C2×D56 | D4 | semidirect |
| 67. C7×M32 | D4 | semidirect |
| 71. C2×C7×C16 | D4 | semidirect |
| 87. #1379 | D7 | semidirect |
| 248. M32 | D28 | semidirect |
| 252. C2×C16 | D28 | semidirect |
| 385. C7 | #13336 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89680 | 2 |
| C22×D112 | 2 |
| #11736010 | 2 |
| C2×#89311 | 2 |
| C2×#89305 | 2 |
| #11727657 | 2 |
| C7×#1379 | 2 |
| #13336 | 7 |