Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
342 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 1. C22×C11⋊C32 | C2 | semidirect |
| 2. C2×#10622142 | C2 | semidirect |
| 3. #13066794 | C2 | direct (N × H) |
| 8. C2×C11×D16 | C4 | semidirect |
| 13. #10622142 | C22 | semidirect |
| 15. C2×C11⋊C32 | C22 | semidirect |
| 25. C11×D16 | C2×C4 | semidirect |
| 77. C2×D16 | Dic11 | semidirect |
| 106. D16 | C2×Dic11 | semidirect |
| 115. C2×C11 | #1415 | semidirect |
| 138. C11 | C2×#1415 | semidirect |
| 169. C2 | #13066794 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C11⋊C32 | 2 |
| C2×#10622142 | 2 |
| #13066794 | 2 |
| C22×C11×D16 | 2 |
| C2×#1415 | 11 |