Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
794 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 794 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×#3036 | C2 | semidirect |
| 2. #11740747 | C2 | semidirect |
| 3. #11739823 | C2 | semidirect |
| 4. #11729565 | C2 | semidirect |
| 5. #11729351 | C2 | semidirect |
| 6. #11728256 | C2 | semidirect |
| 7. #11725521 | C2 | semidirect |
| 44. C7×C4⋊Q8 | D4 | semidirect |
| 45. C7×#127 | D4 | semidirect |
| 70. C7×C4⋊C8 | D4 | semidirect |
| 78. C4⋊(C7⋊C8) | D4 | semidirect |
| 82. #3036 | D7 | semidirect |
| 104. C2×C7×D4 | D8 | semidirect |
| 247. C4⋊Q8 | C22⋊D7 | semidirect |
| 254. #127 | C22⋊D7 | semidirect |
| 274. C4⋊C8 | C22⋊D7 | semidirect |
| 343. C2×D4 | #1141 | semidirect |
| 443. C7 | #10238 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3036 | 2 |
| #11740747 | 2 |
| #11739823 | 2 |
| #11729565 | 2 |
| #11729351 | 2 |
| #11728256 | 2 |
| #11725521 | 2 |
| #10238 | 7 |