Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
658 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 658 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 |
|---|---|---|
| 2. #11740762 | C2 | semidirect |
| 3. #11739824 | C2 | semidirect |
| 4. #11729565 | C2 | semidirect |
| 5. #11729351 | C2 | semidirect |
| 6. #11728261 | C2 | semidirect |
| 7. #11725521 | C2 | semidirect |
| 101. C2×C7×D4 | SD16 | semidirect |
| 305. C2×D4 | #1142 | semidirect |
| 400. C7 | #10240 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3036 | 2 |
| #11740762 | 2 |
| #11739824 | 2 |
| #11729565 | 2 |
| #11729351 | 2 |
| #11728261 | 2 |
| #11725521 | 2 |
| #10240 | 7 |