Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
834 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 834 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×#10622529 | C2 | semidirect |
| 2. #13079045 | C2 | semidirect |
| 3. #13079043 | C2 | semidirect |
| 4. #13070876 | C2 | semidirect |
| 5. #13070872 | C2 | semidirect |
| 6. #13070868 | C2 | semidirect |
| 7. #13070865 | C2 | semidirect |
| 8. C4×C16×D11 | C2 | semidirect |
| 9. C11×#2248 | C2 | semidirect |
| 77. C16×D11 | D4 | semidirect |
| 127. #2248 | D11 | semidirect |
| 195. C4×C11 | #508 | semidirect |
| 291. C11 | #33713 | semidirect |
| 333. C4 | #10622529 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10622529 | 2 |
| #13079045 | 2 |
| #13079043 | 2 |
| #13070876 | 2 |
| #13070872 | 2 |
| #13070868 | 2 |
| #13070865 | 2 |
| C4×C16×D11 | 2 |
| C11×#2248 | 2 |
| #33713 | 11 |