Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
432 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 432 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×#89309 | C2 | semidirect |
| 4. #11728403 | C2 | semidirect |
| 5. #11728332 | C2 | semidirect |
| 6. C2×#89283 | C2 | semidirect |
| 7. C7×#1386 | C2 | semidirect |
| 71. #6386 | D4 | semidirect |
| 83. #1386 | D7 | semidirect |
| 384. C7 | #13386 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11736626 | 2 |
| #11729193 | 2 |
| C2×#89309 | 2 |
| #11728403 | 2 |
| #11728332 | 2 |
| C2×#89283 | 2 |
| C7×#1386 | 2 |
| #13386 | 7 |