Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
506 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 506 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×#3395 | C2 | semidirect |
| 4. #11729064 | C2 | semidirect |
| 5. Q8×C7⋊C16 | C2 | semidirect |
| 6. #11728664 | C2 | semidirect |
| 47. #3395 | D7 | semidirect |
| 98. C7×Q8 | SD32 | semidirect |
| 178. Q8 | #6402 | semidirect |
| 191. C7 | #33926 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3395 | 2 |
| Q8×D56 | 2 |
| #11729069 | 2 |
| #11729064 | 2 |
| Q8×C7⋊C16 | 2 |
| #11728664 | 2 |
| C4×#6402 | 2 |
| #33926 | 7 |