Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
562 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 562 conjugacy classes of subgroups — too many to draw. Only its 165 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 |
|---|---|---|
| 1. C7×#3391 | C2 | semidirect |
| 2. Q8×D56 | C2 | semidirect |
| 3. #11729047 | C2 | semidirect |
| 4. #11729042 | C2 | semidirect |
| 5. Q8×C7⋊C16 | C2 | semidirect |
| 6. #11728640 | C2 | semidirect |
| 7. C4×#6400 | C2 | semidirect |
| 47. #3391 | D7 | semidirect |
| 77. D56 | #41 | semidirect |
| 98. C7×Q8 | D16 | semidirect |
| 185. Q8 | #6400 | semidirect |
| 202. C7 | #33925 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3391 | 2 |
| Q8×D56 | 2 |
| #11729047 | 2 |
| #11729042 | 2 |
| Q8×C7⋊C16 | 2 |
| #11728640 | 2 |
| C4×#6400 | 2 |
| #33925 | 7 |