Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
794 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 101 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. #11740742 | C2 | semidirect |
| 3. #11731244 | C2 | semidirect |
| 4. C7×#1502 | C2 | semidirect |
| 5. #11728528 | C2 | semidirect |
| 6. #11728511 | C2 | semidirect |
| 7. #11725426 | C2 | semidirect |
| 39. C7×C4⋊Q8 | D4 | semidirect |
| 40. C7×#127 | D4 | semidirect |
| 78. C4⋊(C7⋊C8) | D4 | semidirect |
| 79. C4⋊(C7⋊C8) | D4 | semidirect |
| 85. #1502 | D7 | semidirect |
| 125. C2×D28 | D8 | semidirect |
| 247. C4⋊Q8 | D28 | semidirect |
| 254. #127 | D28 | semidirect |
| 443. C7 | #10238 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11740747 | 2 |
| #11740742 | 2 |
| #11731244 | 2 |
| C7×#1502 | 2 |
| #11728528 | 2 |
| #11728511 | 2 |
| #11725426 | 2 |
| #10238 | 7 |