Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
300 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 67 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. #11728699 | C2 | semidirect |
| 3. #11727050 | C2 | semidirect |
| 5. C7×Q8⋊C16 | C2 | semidirect |
| 7. #11725311 | C2 | semidirect |
| 58. Q8⋊C16 | D7 | semidirect |
| 234. C7 | #12385 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11737360 | 2 |
| #11728699 | 2 |
| #11727050 | 2 |
| #11726812 | 2 |
| C7×Q8⋊C16 | 2 |
| #11725366 | 2 |
| #11725311 | 2 |
| #12385 | 7 |