Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
500 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 91 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. C4×#6408 | C2 | semidirect |
| 3. #11729354 | C2 | semidirect |
| 4. #11725452 | C2 | semidirect |
| 5. #11725451 | C2 | semidirect |
| 6. C2×C7×#124 | C4 | semidirect |
| 9. C7×#393 | C4 | semidirect |
| 12. C7×#392 | C4 | semidirect |
| 16. C7×#383 | C4 | semidirect |
| 111. C2×#124 | Dic7 | semidirect |
| 116. #393 | Dic7 | semidirect |
| 119. #392 | Dic7 | semidirect |
| 123. #383 | Dic7 | semidirect |
| 354. C7 | #11730 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2631 | 2 |
| C4×#6408 | 2 |
| #11729354 | 2 |
| #11725452 | 2 |
| #11725451 | 2 |
| #11730 | 7 |