Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
814 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 814 conjugacy classes of subgroups — too many to draw. Only its 179 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×#10622528 | C2 | semidirect |
| 3. D11×#494 | C2 | semidirect |
| 4. #13070886 | C2 | semidirect |
| 5. #13070871 | C2 | semidirect |
| 6. #13070869 | C2 | semidirect |
| 7. #13070868 | C2 | semidirect |
| 8. C4×#66862 | C2 | semidirect |
| 9. C11×#2248 | C2 | semidirect |
| 77. #66862 | D4 | semidirect |
| 127. #2248 | D11 | semidirect |
| 192. C4×C11 | #510 | semidirect |
| 288. C11 | #33718 | semidirect |
| 328. C4 | #10622528 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10622528 | 2 |
| #13079043 | 2 |
| D11×#494 | 2 |
| #13070886 | 2 |
| #13070871 | 2 |
| #13070869 | 2 |
| #13070868 | 2 |
| C4×#66862 | 2 |
| C11×#2248 | 2 |
| #33718 | 11 |