Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
3550 conjugacy classes of subgroups; only the 667 normal subgroups are shown.
This group has 3550 conjugacy classes of subgroups — too many to draw. Only its 667 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. #13076869 | C2 | direct (N × H) |
| 2. C2×#10622560 | C2 | semidirect |
| 6. C23×Dic22 | C22 | semidirect |
| 11. C2×C11⋊#95 | C22 | semidirect |
| 12. #10622560 | C22 | semidirect |
| 14. C25×C11 | Q8 | semidirect |
| 20. C22×Dic22 | C23 | semidirect |
| 25. C11⋊#95 | C23 | semidirect |
| 33. C24×C11 | C2×Q8 | semidirect |
| 85. C25 | Dic22 | semidirect |
| 98. C2×C11 | #2840 | semidirect |
| 107. C24 | C2×Dic22 | semidirect |
| 118. C11 | C2×#2840 | semidirect |
| 148. C2 | #13076869 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13076869 | 2 |
| C2×#10622560 | 2 |
| C2×#10622860 | 2 |
| C2×C11×#379 | 2 |
| C2×#2840 | 11 |