Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
3342 conjugacy classes of subgroups; only the 739 normal subgroups are shown.
This group has 3342 conjugacy classes of subgroups — too many to draw. Only its 739 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×#10622552 | C2 | semidirect |
| 3. C2×#10622548 | C2 | semidirect |
| 4. C2×C43×C11 | C2 | semidirect |
| 12. C2×#66927 | C4 | semidirect |
| 30. C2×C42×C11 | D4 | semidirect |
| 58. C42×C11 | C22⋊C4 | semidirect |
| 64. C2×C43 | D11 | semidirect |
| 84. C2×C4×C11 | #127 | semidirect |
| 112. C4×C11 | #390 | semidirect |
| 131. C2×C42 | D44 | semidirect |
| 163. C42 | (C2×D11)⋊C4 | semidirect |
| 164. C11 | #14713 | semidirect |
| 184. C2×C4 | #66927 | semidirect |
| 202. C4 | #10622552 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#66927 | 2 |
| C2×#10622552 | 2 |
| C2×#10622548 | 2 |
| C2×C43×C11 | 2 |
| #14713 | 11 |