Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
454 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 454 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. C7×#2143 | C2 | semidirect |
| 3. #11729835 | C2 | semidirect |
| 4. C2×#89311 | C2 | semidirect |
| 5. #11728461 | C2 | semidirect |
| 6. C2×#89290 | C2 | semidirect |
| 7. #11725620 | C2 | semidirect |
| 60. C7×#108 | D4 | semidirect |
| 73. #2143 | D7 | semidirect |
| 217. #108 | C22⋊D7 | semidirect |
| 326. C7 | #13417 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11741351 | 2 |
| C7×#2143 | 2 |
| #11729835 | 2 |
| C2×#89311 | 2 |
| #11728461 | 2 |
| C2×#89290 | 2 |
| #11725620 | 2 |
| #13417 | 7 |