Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
552 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 171 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. #13070835 | C2 | direct (N × H) |
| 3. C2×#10622132 | C2 | semidirect |
| 4. C2×#10622134 | C2 | semidirect |
| 21. #10622134 | C22 | semidirect |
| 22. #10622132 | C22 | semidirect |
| 195. C2×C11 | #2239 | semidirect |
| 235. C11 | C2×#2239 | semidirect |
| 285. C2 | #13070835 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10622750 | 2 |
| #13070835 | 2 |
| C2×#10622132 | 2 |
| C2×#10622134 | 2 |
| C2×#10622191 | 2 |
| C2×C11×#430 | 2 |
| C2×#2239 | 11 |