Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
454 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 454 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 |
|---|---|---|
| 2. #11729835 | C2 | semidirect |
| 3. #11729834 | C2 | semidirect |
| 4. C2×#89358 | C2 | semidirect |
| 5. C2×#89358 | C2 | semidirect |
| 6. #11727655 | C2 | semidirect |
| 7. #11725478 | C2 | semidirect |
| 62. #6393 | D4 | semidirect |
| 326. C7 | #13417 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3155 | 2 |
| #11729835 | 2 |
| #11729834 | 2 |
| C2×#89358 | 2 |
| #11727655 | 2 |
| #11725478 | 2 |
| #13417 | 7 |