Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
636 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 636 conjugacy classes of subgroups — too many to draw. Only its 101 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×#3100 | C2 | semidirect |
| 2. #11740731 | C2 | semidirect |
| 3. #11739753 | C2 | semidirect |
| 4. #11729554 | C2 | semidirect |
| 5. #11729369 | C2 | semidirect |
| 6. #11728512 | C2 | semidirect |
| 7. #11725546 | C2 | semidirect |
| 88. #3100 | D7 | semidirect |
| 149. C2×C7⋊C8 | D8 | semidirect |
| 410. C7 | #10032 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3100 | 2 |
| #11740731 | 2 |
| #11739753 | 2 |
| #11729554 | 2 |
| #11729369 | 2 |
| #11728512 | 2 |
| #11725546 | 2 |
| #10032 | 7 |