Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1134 conjugacy classes of subgroups; only the 371 normal subgroups are shown.
This group has 1134 conjugacy classes of subgroups — too many to draw. Only its 371 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×#1839 | C2 | semidirect |
| 3. #11727147 | C2 | semidirect |
| 5. #11726361 | C2 | semidirect |
| 36. C42×D7 | C8 | semidirect |
| 40. #1839 | D7 | direct (N × H) |
| 59. C42×C7 | C2×C8 | semidirect |
| 66. C4×Dic7 | C2×C8 | semidirect |
| 160. C42 | C8×D7 | semidirect |
| 164. D7 | #1839 | direct (N × H) |
| 188. C7 | C2×#1839 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C43×D7 | 2 |
| C7×#1839 | 2 |
| #11727147 | 2 |
| D7×#336 | 2 |
| #11726361 | 2 |
| C2×#1839 | 7 |