Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
212 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 3. #11726278 | C2 | semidirect |
| 4. C7×#1368 | C2 | semidirect |
| 5. #11725317 | C2 | semidirect |
| 6. #11725272 | C2 | semidirect |
| 48. #1368 | D7 | semidirect |
| 73. C7×C16 | M16 | semidirect |
| 164. C16 | #1131 | semidirect |
| 189. C7 | #12087 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11726831 | 2 |
| #11726279 | 2 |
| #11726278 | 2 |
| C7×#1368 | 2 |
| #11725317 | 2 |
| #11725272 | 2 |
| #11725271 | 2 |
| #12087 | 7 |