Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
2222 conjugacy classes of subgroups; only the 667 normal subgroups are shown.
This group has 2222 conjugacy classes of subgroups — too many to draw. Only its 667 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. #13074576 | C2 | direct (N × H) |
| 2. C2×#10622288 | C2 | semidirect |
| 3. C2×#10622289 | C2 | semidirect |
| 5. C2×#10622541 | C2 | semidirect |
| 6. C2×C11×#376 | C2 | semidirect |
| 13. C11×#376 | C22 | semidirect |
| 18. #10622541 | C22 | semidirect |
| 19. #10622289 | C22 | semidirect |
| 20. #10622288 | C22 | semidirect |
| 73. C2×#376 | D11 | semidirect |
| 109. #376 | C2×D11 | semidirect |
| 147. C2×C11 | #2644 | semidirect |
| 178. C11 | C2×#2644 | semidirect |
| 219. C2 | #13074576 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13074576 | 2 |
| C2×#10622288 | 2 |
| C2×#10622289 | 2 |
| C2×#10622552 | 2 |
| C2×#10622541 | 2 |
| C2×C11×#376 | 2 |
| C2×#2644 | 11 |