Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
594 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 594 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 |
|---|---|---|
| 1. C7×#3150 | C2 | semidirect |
| 2. C2×#89965 | C2 | semidirect |
| 3. C2×#89361 | C2 | semidirect |
| 4. #11727579 | C2 | semidirect |
| 5. #11725470 | C2 | semidirect |
| 50. C2×D56 | D4 | semidirect |
| 57. #6386 | D4 | semidirect |
| 60. #3150 | D7 | semidirect |
| 298. C7 | #13341 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3150 | 2 |
| C2×#89965 | 2 |
| C2×#89361 | 2 |
| #11727579 | 2 |
| #11725470 | 2 |
| #13341 | 7 |