Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
552 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 552 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. #11741250 | C2 | semidirect |
| 2. #11741244 | C2 | semidirect |
| 3. C2×#89680 | C2 | semidirect |
| 4. C7×#2117 | C2 | semidirect |
| 5. #11729204 | C2 | semidirect |
| 6. C2×#89311 | C2 | semidirect |
| 7. #11725628 | C2 | semidirect |
| 54. C2×Dic28 | D4 | semidirect |
| 65. C2×D56 | D4 | semidirect |
| 70. C7×M32 | D4 | semidirect |
| 77. #6393 | D4 | semidirect |
| 87. #2117 | D7 | semidirect |
| 256. M32 | C22⋊D7 | semidirect |
| 396. C7 | #13310 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11741250 | 2 |
| #11741244 | 2 |
| C2×#89680 | 2 |
| C7×#2117 | 2 |
| #11729204 | 2 |
| C2×#89311 | 2 |
| #11725628 | 2 |
| #13310 | 7 |