Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
440 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 97 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. C7×#1546 | C2 | semidirect |
| 3. #11729527 | C2 | semidirect |
| 5. #11728503 | C2 | semidirect |
| 7. #11725520 | C2 | semidirect |
| 66. #1546 | D7 | semidirect |
| 314. C7 | #10445 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89855 | 2 |
| C7×#1546 | 2 |
| #11729527 | 2 |
| #11728510 | 2 |
| #11728503 | 2 |
| #11728281 | 2 |
| #11725520 | 2 |
| #10445 | 7 |