Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
462 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 462 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 |
|---|---|---|
| 2. C2×C7×#359 | C2 | semidirect |
| 3. #11729832 | C2 | semidirect |
| 4. C2×#89304 | C2 | semidirect |
| 5. #11728455 | C2 | semidirect |
| 6. C2×#89290 | C2 | semidirect |
| 7. #11725611 | C2 | semidirect |
| 61. C7×#108 | D4 | semidirect |
| 73. C2×#359 | D7 | semidirect |
| 224. #108 | C22⋊D7 | semidirect |
| 350. C7 | #13411 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11741351 | 2 |
| C2×C7×#359 | 2 |
| #11729832 | 2 |
| C2×#89304 | 2 |
| #11728455 | 2 |
| C2×#89290 | 2 |
| #11725611 | 2 |
| #13411 | 7 |