Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
522 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 107 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. #13077416 | C2 | semidirect |
| 3. C2×#10622126 | C2 | semidirect |
| 4. #13070331 | C2 | semidirect |
| 5. #13069490 | C2 | semidirect |
| 6. #13066699 | C2 | semidirect |
| 7. C11×#1386 | C2 | semidirect |
| 20. #10622521 | C4 | semidirect |
| 46. C2×D88 | C2×C4 | semidirect |
| 55. C11×M32 | C2×C4 | semidirect |
| 112. Dic44 | C22⋊C4 | semidirect |
| 118. D88 | C22⋊C4 | semidirect |
| 128. #1386 | D11 | semidirect |
| 237. M32 | C4×D11 | semidirect |
| 306. C11 | #13025 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10622521 | 2 |
| #13077416 | 2 |
| C2×#10622126 | 2 |
| #13070331 | 2 |
| #13069490 | 2 |
| #13066699 | 2 |
| C11×#1386 | 2 |
| #13025 | 11 |