Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
3798 conjugacy classes of subgroups; only the 1179 normal subgroups are shown.
This group has 3798 conjugacy classes of subgroups — too many to draw. Only its 1179 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. #13071793 | C2 | direct (N × H) |
| 2. C2×#10622833 | C2 | semidirect |
| 3. C2×#10622550 | C2 | semidirect |
| 7. C2×C11×#127 | C4 | semidirect |
| 11. #10622833 | C22 | semidirect |
| 13. #10622550 | C22 | semidirect |
| 17. C22×D4×C11 | C2×C4 | semidirect |
| 23. C11×#127 | C2×C4 | semidirect |
| 24. C2×C42×C11 | C2×C4 | semidirect |
| 38. C2×D4×C11 | C22×C4 | semidirect |
| 46. C42×C11 | C22×C4 | semidirect |
| 70. C2×#127 | Dic11 | semidirect |
| 90. C22×D4 | C2×Dic11 | semidirect |
| 96. #127 | C2×Dic11 | semidirect |
| 99. C2×C42 | C2×Dic11 | semidirect |
| 103. C2×C11 | #2380 | semidirect |
| 114. C2×D4 | C22×Dic11 | semidirect |
| 123. C42 | C22×Dic11 | semidirect |
| 124. C11 | C2×#2380 | semidirect |
| 152. C2 | #13071793 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13071793 | 2 |
| C2×#10622833 | 2 |
| C2×#10622550 | 2 |
| C22×C11×#127 | 2 |
| C2×#2380 | 11 |