Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
234 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 234 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 |
|---|---|---|
| 2. #11728632 | C2 | semidirect |
| 3. #11726279 | C2 | semidirect |
| 4. C7×#1333 | C2 | semidirect |
| 5. #11725322 | C2 | semidirect |
| 6. #11725317 | C2 | semidirect |
| 7. #11725270 | C2 | semidirect |
| 50. #1333 | D7 | semidirect |
| 57. C7×D8 | M16 | semidirect |
| 154. D8 | #1131 | semidirect |
| 198. C7 | #12078 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11728639 | 2 |
| #11728632 | 2 |
| #11726279 | 2 |
| C7×#1333 | 2 |
| #11725322 | 2 |
| #11725317 | 2 |
| #11725270 | 2 |
| #12078 | 7 |