Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
402 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 73 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×#1557 | C2 | semidirect |
| 3. #11729551 | C2 | semidirect |
| 4. #11728558 | C2 | semidirect |
| 5. #11728277 | C2 | semidirect |
| 6. #11728246 | C2 | semidirect |
| 7. #11725560 | C2 | semidirect |
| 79. #1557 | D7 | semidirect |
| 350. C7 | #10496 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11740751 | 2 |
| C7×#1557 | 2 |
| #11729551 | 2 |
| #11728558 | 2 |
| #11728277 | 2 |
| #11728246 | 2 |
| #11725560 | 2 |
| #10496 | 7 |