Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
914 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 914 conjugacy classes of subgroups — too many to draw. Only its 267 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. C2×#10622295 | C2 | semidirect |
| 2. C2×#10622312 | C2 | semidirect |
| 5. #13068287 | C2 | direct (N × H) |
| 6. C2×C11×#322 | C2 | semidirect |
| 17. #10622312 | C22 | semidirect |
| 23. #10622295 | C22 | semidirect |
| 24. C11×#322 | C22 | semidirect |
| 93. C2×#322 | D11 | semidirect |
| 135. #322 | C2×D11 | semidirect |
| 178. C2×C11 | #1722 | semidirect |
| 214. C11 | C2×#1722 | semidirect |
| 252. C2 | #13068287 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10622295 | 2 |
| C2×#10622312 | 2 |
| C2×#10622306 | 2 |
| C2×#10622307 | 2 |
| #13068287 | 2 |
| C2×C11×#322 | 2 |
| C2×#1722 | 11 |