Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
2130 conjugacy classes of subgroups; only the 667 normal subgroups are shown.
This group has 2130 conjugacy classes of subgroups — too many to draw. Only its 667 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. C2×C43×C7 | C2 | semidirect |
| 2. #11739523 | C2 | semidirect |
| 4. #11739514 | C2 | semidirect |
| 5. #11730759 | C2 | semidirect |
| 6. #11730754 | C2 | semidirect |
| 7. C4×#6439 | C2 | semidirect |
| 54. C2×C43 | D7 | semidirect |
| 73. C42×C7 | #41 | semidirect |
| 104. C2×C4×C7 | #126 | semidirect |
| 171. C42 | #1157 | semidirect |
| 191. C2×C4 | #6439 | semidirect |
| 195. C7 | #36641 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C43×C7 | 2 |
| #11739523 | 2 |
| #11739515 | 2 |
| #11739514 | 2 |
| #11730759 | 2 |
| #11730754 | 2 |
| C4×#6439 | 2 |
| #36641 | 7 |