Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
566 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 566 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 |
|---|---|---|
| 2. C2×#89967 | C2 | semidirect |
| 3. C22×#6401 | C2 | semidirect |
| 4. C2×#89362 | C2 | semidirect |
| 5. C2×#89358 | C2 | semidirect |
| 6. #11727658 | C2 | semidirect |
| 7. #11725477 | C2 | semidirect |
| 65. C2×Dic28 | D4 | semidirect |
| 75. #6386 | D4 | semidirect |
| 79. C2×C7⋊C16 | D4 | semidirect |
| 379. C7 | #13338 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3155 | 2 |
| C2×#89967 | 2 |
| C22×#6401 | 2 |
| C2×#89362 | 2 |
| C2×#89358 | 2 |
| #11727658 | 2 |
| #11725477 | 2 |
| #13338 | 7 |