Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
552 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 97 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×#89932 | C2 | semidirect |
| 2. C2×#89919 | C2 | semidirect |
| 3. #11736595 | C2 | semidirect |
| 4. C2×C7×#357 | C2 | semidirect |
| 5. C2×#89305 | C2 | semidirect |
| 6. C2×#89303 | C2 | semidirect |
| 7. #11725529 | C2 | semidirect |
| 40. C2×C7×D8 | D4 | semidirect |
| 76. #6393 | D4 | semidirect |
| 78. #6386 | D4 | semidirect |
| 86. C2×#357 | D7 | semidirect |
| 237. C2×D8 | D28 | semidirect |
| 405. C7 | #13307 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89932 | 2 |
| C2×#89919 | 2 |
| #11736595 | 2 |
| C2×C7×#357 | 2 |
| C2×#89305 | 2 |
| C2×#89303 | 2 |
| #11725529 | 2 |
| #13307 | 7 |