Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
610 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 610 conjugacy classes of subgroups — too many to draw. Only its 105 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×#2547 | C2 | semidirect |
| 2. #11740660 | C2 | semidirect |
| 4. #11729527 | C2 | semidirect |
| 5. #11729351 | C2 | semidirect |
| 6. #11727223 | C2 | semidirect |
| 7. #11725426 | C2 | semidirect |
| 82. #2547 | D7 | semidirect |
| 410. C7 | #10239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2547 | 2 |
| #11740660 | 2 |
| #11739752 | 2 |
| #11729527 | 2 |
| #11729351 | 2 |
| #11727223 | 2 |
| #11725426 | 2 |
| #10239 | 7 |