Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
492 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 492 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. C7×#1800 | C2 | semidirect |
| 3. #11729351 | C2 | semidirect |
| 4. #11728256 | C2 | semidirect |
| 5. #11728256 | C2 | semidirect |
| 6. #11728247 | C2 | semidirect |
| 7. #11725520 | C2 | semidirect |
| 63. #1800 | D7 | semidirect |
| 335. C7 | #10441 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89787 | 2 |
| C7×#1800 | 2 |
| #11729351 | 2 |
| #11728256 | 2 |
| #11728247 | 2 |
| #11725520 | 2 |
| #10441 | 7 |