Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
408 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 91 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. #11729193 | C2 | semidirect |
| 3. C2×#89310 | C2 | semidirect |
| 4. #11728475 | C2 | semidirect |
| 5. C2×#89292 | C2 | semidirect |
| 6. C2×#89284 | C2 | semidirect |
| 7. C7×#1387 | C2 | semidirect |
| 66. C2×C7⋊C16 | D4 | semidirect |
| 75. #1387 | D7 | semidirect |
| 340. C7 | #13384 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11736595 | 2 |
| #11729193 | 2 |
| C2×#89310 | 2 |
| #11728475 | 2 |
| C2×#89292 | 2 |
| C2×#89284 | 2 |
| C7×#1387 | 2 |
| #13384 | 7 |