Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
322 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 73 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×#1670 | C2 | semidirect |
| 4. #11729064 | C2 | semidirect |
| 5. Q8⋊(C7⋊C16) | C2 | semidirect |
| 6. #11725281 | C2 | semidirect |
| 57. #1670 | D7 | semidirect |
| 114. C7×Q8 | SD32 | semidirect |
| 221. Q8 | #6402 | semidirect |
| 240. C7 | #12356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D56 | 2 |
| C7×#1670 | 2 |
| #11729069 | 2 |
| #11729064 | 2 |
| Q8⋊(C7⋊C16) | 2 |
| #11725281 | 2 |
| #11725277 | 2 |
| #12356 | 7 |