Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
274 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 274 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 |
|---|---|---|
| 21. #10622131 | C4 | semidirect |
| 200. C11 | #13171 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10622131 | 2 |
| C2×#10622127 | 2 |
| #13070215 | 2 |
| #13069402 | 2 |
| #13069399 | 2 |
| #13066725 | 2 |
| C11×#1387 | 2 |
| #13171 | 11 |