Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
568 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 568 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 |
|---|---|---|
| 1. #11741351 | C2 | semidirect |
| 2. #11741339 | C2 | semidirect |
| 3. C2×#89680 | C2 | semidirect |
| 4. C7×#2145 | C2 | semidirect |
| 5. #11728412 | C2 | semidirect |
| 6. #11728406 | C2 | semidirect |
| 7. #11725620 | C2 | semidirect |
| 56. C2×Dic28 | D4 | semidirect |
| 67. C2×D56 | D4 | semidirect |
| 70. C7×M32 | D4 | semidirect |
| 82. C2×C7⋊C16 | D4 | semidirect |
| 90. #2145 | D7 | semidirect |
| 267. M32 | C22⋊D7 | semidirect |
| 407. C7 | #13334 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11741351 | 2 |
| #11741339 | 2 |
| C2×#89680 | 2 |
| C7×#2145 | 2 |
| #11728412 | 2 |
| #11728406 | 2 |
| #11725620 | 2 |
| #13334 | 7 |