Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
684 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 83 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. #13079621 | C2 | semidirect |
| 2. #13078990 | C2 | semidirect |
| 4. #13067215 | C2 | semidirect |
| 5. #13067129 | C2 | semidirect |
| 6. #13066508 | C2 | semidirect |
| 7. C11×#1555 | C2 | semidirect |
| 59. #66922 | D4 | semidirect |
| 60. #66922 | D4 | semidirect |
| 64. C11×C4⋊C8 | D4 | semidirect |
| 75. #66867 | D4 | semidirect |
| 133. #1555 | D11 | semidirect |
| 258. C4⋊C8 | C22⋊D11 | semidirect |
| 329. C11 | #10096 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13079621 | 2 |
| #13078990 | 2 |
| #13074723 | 2 |
| #13067215 | 2 |
| #13067129 | 2 |
| #13066508 | 2 |
| C11×#1555 | 2 |
| #10096 | 11 |