Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
492 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 492 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. C7×#1545 | C2 | semidirect |
| 3. #11729513 | C2 | semidirect |
| 4. #11728511 | C2 | semidirect |
| 5. #11728281 | C2 | semidirect |
| 6. #11728247 | C2 | semidirect |
| 7. #11725551 | C2 | semidirect |
| 66. #1545 | 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×#89844 | 2 |
| C7×#1545 | 2 |
| #11729513 | 2 |
| #11728511 | 2 |
| #11728281 | 2 |
| #11728247 | 2 |
| #11725551 | 2 |
| #10441 | 7 |