Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
636 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 636 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. #11740743 | C2 | semidirect |
| 3. #11729554 | C2 | semidirect |
| 4. #11727591 | C2 | semidirect |
| 5. #11725466 | C2 | semidirect |
| 54. #3150 | D7 | semidirect |
| 83. C2×C7×C8 | D8 | semidirect |
| 223. C2×C8 | #1141 | semidirect |
| 271. C7 | #10032 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3150 | 2 |
| #11740743 | 2 |
| #11729554 | 2 |
| #11727591 | 2 |
| #11725466 | 2 |
| #10032 | 7 |