Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
950 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 950 conjugacy classes of subgroups — too many to draw. Only its 111 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. #11740747 | C2 | semidirect |
| 2. #11730763 | C2 | semidirect |
| 3. C7×#1962 | C2 | semidirect |
| 4. #11728256 | C2 | semidirect |
| 5. #11725417 | C2 | semidirect |
| 26. C7×C4⋊Q8 | D4 | semidirect |
| 27. C7×#127 | D4 | semidirect |
| 46. C4⋊(C7⋊C8) | D4 | semidirect |
| 50. #1962 | D7 | semidirect |
| 82. C42×C7 | D8 | semidirect |
| 140. C4⋊Q8 | D28 | semidirect |
| 148. #127 | D28 | semidirect |
| 208. C42 | #1141 | semidirect |
| 249. C7 | #10280 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11740747 | 2 |
| #11730763 | 2 |
| C7×#1962 | 2 |
| #11728256 | 2 |
| #11725417 | 2 |
| #10280 | 7 |