Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
536 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 536 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. #11741352 | C2 | semidirect |
| 3. C2×#89967 | C2 | semidirect |
| 4. #11729840 | C2 | semidirect |
| 5. #11729830 | C2 | semidirect |
| 6. #11729199 | C2 | semidirect |
| 7. #11725619 | C2 | semidirect |
| 399. C7 | #13335 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3414 | 2 |
| #11741352 | 2 |
| C2×#89967 | 2 |
| #11729840 | 2 |
| #11729830 | 2 |
| #11729199 | 2 |
| #11725619 | 2 |
| #13335 | 7 |