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. C2×#10622132 | C2 | semidirect |
| 4. #13069404 | C2 | semidirect |
| 5. #13066715 | C2 | semidirect |
| 6. #13066703 | C2 | semidirect |
| 23. #10622205 | C4 | semidirect |
| 54. #66883 | C2×C4 | semidirect |
| 61. C2×C11⋊C16 | C2×C4 | semidirect |
| 255. C11 | #12949 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13077500 | 2 |
| C2×#10622132 | 2 |
| #13070344 | 2 |
| #13069404 | 2 |
| #13066715 | 2 |
| #13066703 | 2 |
| C11×#2148 | 2 |
| #12949 | 11 |