Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 101 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. #11741339 | C2 | semidirect |
| 3. #11729834 | C2 | semidirect |
| 4. #11727599 | C2 | semidirect |
| 5. #11725469 | C2 | semidirect |
| 47. C2×Dic28 | D4 | semidirect |
| 50. C2×D56 | D4 | semidirect |
| 61. C2×C7⋊C16 | D4 | semidirect |
| 64. #3150 | D7 | semidirect |
| 305. C7 | #13340 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3150 | 2 |
| #11741339 | 2 |
| #11729834 | 2 |
| #11727599 | 2 |
| #11725469 | 2 |
| #13340 | 7 |