Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
322 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
| 5. #11725599 | C2 | semidirect |
| 6. Q8⋊(C7⋊C16) | C2 | semidirect |
| 7. #11725571 | C2 | semidirect |
| 55. #3395 | D7 | semidirect |
| 120. C7×Q8 | SD32 | semidirect |
| 227. Q8 | #6402 | semidirect |
| 246. C7 | #12330 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3395 | 2 |
| #11729067 | 2 |
| #11728693 | 2 |
| #11728668 | 2 |
| #11725599 | 2 |
| Q8⋊(C7⋊C16) | 2 |
| #11725571 | 2 |
| #12330 | 7 |