Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
1022 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 1022 conjugacy classes of subgroups — too many to draw. Only its 251 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×#66890 | C2 | semidirect |
| 2. C2×#10622308 | C2 | semidirect |
| 3. #13070865 | C2 | direct (N × H) |
| 4. C2×C4×C11⋊C16 | C2 | semidirect |
| 5. C2×C11×#493 | C2 | semidirect |
| 13. C11×#493 | C22 | semidirect |
| 16. C2×#66890 | C22 | semidirect |
| 19. #10622308 | C22 | semidirect |
| 20. C4×C11⋊C16 | C22 | semidirect |
| 45. C2×C11⋊C16 | D4 | semidirect |
| 77. C11⋊C16 | C2×D4 | semidirect |
| 80. C2×#493 | D11 | semidirect |
| 94. C2×C4×C11 | D16 | semidirect |
| 119. #493 | C2×D11 | semidirect |
| 132. C4×C11 | C2×D16 | semidirect |
| 162. C2×C11 | #2246 | semidirect |
| 196. C11 | C2×#2246 | semidirect |
| 212. C2×C4 | #66890 | semidirect |
| 231. C4 | C2×#66890 | semidirect |
| 236. C2 | #13070865 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#66890 | 2 |
| C2×#10622308 | 2 |
| #13070865 | 2 |
| C2×C4×C11⋊C16 | 2 |
| C2×C11×#493 | 2 |
| C2×#2246 | 11 |