Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
394 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 109 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. #13070389 | C2 | semidirect |
| 3. C2×#10622125 | C2 | semidirect |
| 6. #13066717 | C2 | semidirect |
| 7. C11×#1386 | C2 | semidirect |
| 22. #10622153 | C4 | semidirect |
| 45. C11×M32 | C2×C4 | semidirect |
| 58. C2×C11⋊C16 | C2×C4 | semidirect |
| 109. #1386 | D11 | semidirect |
| 194. M32 | C4×D11 | semidirect |
| 255. C11 | #12934 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13077207 | 2 |
| #13070389 | 2 |
| C2×#10622125 | 2 |
| #13070245 | 2 |
| #13068667 | 2 |
| #13066717 | 2 |
| C11×#1386 | 2 |
| #12934 | 11 |