Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
512 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 512 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. #13077212 | C2 | semidirect |
| 3. #13070333 | C2 | semidirect |
| 4. C2×#10622129 | C2 | semidirect |
| 5. C2×#10622153 | C2 | semidirect |
| 6. #13066713 | C2 | semidirect |
| 7. C11×#1387 | C2 | semidirect |
| 20. #10622510 | C4 | semidirect |
| 44. C2×D88 | C2×C4 | semidirect |
| 60. C11×#108 | C2×C4 | semidirect |
| 129. #1387 | D11 | semidirect |
| 244. #108 | C4×D11 | semidirect |
| 311. C11 | #12996 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10622510 | 2 |
| #13077212 | 2 |
| #13070333 | 2 |
| C2×#10622129 | 2 |
| C2×#10622153 | 2 |
| #13066713 | 2 |
| C11×#1387 | 2 |
| #12996 | 11 |