Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
324 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 103 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. #11727517 | C2 | semidirect |
| 3. #11727498 | C2 | semidirect |
| 4. #11725582 | C2 | semidirect |
| 7. C7×#499 | C4 | semidirect |
| 8. C7×#495 | C4 | semidirect |
| 13. C4×C7×Q16 | C4 | semidirect |
| 15. C4×C7×D8 | C4 | semidirect |
| 97. #499 | Dic7 | semidirect |
| 98. #495 | Dic7 | semidirect |
| 103. C4×Q16 | Dic7 | semidirect |
| 105. C4×D8 | Dic7 | semidirect |
| 259. C7 | #11855 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3168 | 2 |
| #11727517 | 2 |
| #11727498 | 2 |
| #11725582 | 2 |
| #11725580 | 2 |
| #11855 | 7 |