Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
658 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 658 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×#3037 | C2 | semidirect |
| 3. #11739921 | C2 | semidirect |
| 4. #11729565 | C2 | semidirect |
| 5. #11729375 | C2 | semidirect |
| 6. #11728256 | C2 | semidirect |
| 7. #11725521 | C2 | semidirect |
| 81. #3037 | D7 | semidirect |
| 98. C2×C7×Q8 | D8 | semidirect |
| 309. C2×Q8 | #1141 | semidirect |
| 420. C7 | #10242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3037 | 2 |
| #11740747 | 2 |
| #11739921 | 2 |
| #11729565 | 2 |
| #11729375 | 2 |
| #11728256 | 2 |
| #11725521 | 2 |
| #10242 | 7 |