Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
500 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 109 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. #13070344 | C2 | semidirect |
| 4. C2×#10622152 | C2 | semidirect |
| 5. #13066731 | C2 | semidirect |
| 6. #13066730 | C2 | semidirect |
| 7. C11×#2143 | C2 | semidirect |
| 60. C11×#108 | D4 | semidirect |
| 65. #66883 | D4 | semidirect |
| 128. #2143 | D11 | semidirect |
| 244. #108 | C22⋊D11 | semidirect |
| 308. C11 | #12998 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13078221 | 2 |
| C2×#10622506 | 2 |
| #13070344 | 2 |
| C2×#10622152 | 2 |
| #13066731 | 2 |
| #13066730 | 2 |
| C11×#2143 | 2 |
| #12998 | 11 |