Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
244 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 85 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. #13070447 | C2 | semidirect |
| 2. #13070435 | C2 | semidirect |
| 4. #13066570 | C2 | semidirect |
| 5. #13066570 | C2 | semidirect |
| 6. #13066533 | C2 | semidirect |
| 7. C11×#1370 | C2 | semidirect |
| 71. C11⋊C16 | D8 | semidirect |
| 75. #1370 | D11 | semidirect |
| 89. D44 | M32 | semidirect |
| 184. C11 | #12038 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13070447 | 2 |
| #13070435 | 2 |
| C8×D88 | 2 |
| #13066570 | 2 |
| #13066533 | 2 |
| C11×#1370 | 2 |
| #12038 | 11 |