Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
548 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 2. C2×#10622506 | C2 | semidirect |
| 3. C2×#10622154 | C2 | semidirect |
| 4. C2×#10622133 | C2 | semidirect |
| 5. C2×#10622152 | C2 | semidirect |
| 6. #13066714 | C2 | semidirect |
| 7. C11×#1383 | C2 | semidirect |
| 57. C11×#108 | D4 | semidirect |
| 62. #66883 | D4 | semidirect |
| 123. #1383 | D11 | semidirect |
| 235. #108 | D44 | semidirect |
| 294. C11 | #13010 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10622478 | 2 |
| C2×#10622506 | 2 |
| C2×#10622154 | 2 |
| C2×#10622133 | 2 |
| C2×#10622152 | 2 |
| #13066714 | 2 |
| C11×#1383 | 2 |
| #13010 | 11 |