Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
600 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 95 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×#89827 | C2 | semidirect |
| 3. C2×#89486 | C2 | semidirect |
| 4. C2×C7×#329 | C2 | semidirect |
| 5. #11727576 | C2 | semidirect |
| 6. C2×#89259 | C2 | semidirect |
| 7. #11725465 | C2 | semidirect |
| 62. #6432 | D4 | semidirect |
| 66. C7×#97 | D4 | semidirect |
| 76. #6377 | D4 | semidirect |
| 82. C2×#329 | D7 | semidirect |
| 247. #97 | C22⋊D7 | semidirect |
| 382. C7 | #10085 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11740452 | 2 |
| C2×#89827 | 2 |
| C2×#89486 | 2 |
| C2×C7×#329 | 2 |
| #11727576 | 2 |
| C2×#89259 | 2 |
| #11725465 | 2 |
| #10085 | 7 |