Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
592 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 105 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. #13079554 | C2 | semidirect |
| 3. #13067285 | C2 | semidirect |
| 4. #13067019 | C2 | semidirect |
| 5. #13066937 | C2 | semidirect |
| 6. #13066511 | C2 | semidirect |
| 7. C11×#3077 | C2 | semidirect |
| 87. C2×D4×C11 | SD16 | semidirect |
| 134. #3077 | D11 | semidirect |
| 310. C2×D4 | #4325 | semidirect |
| 344. C11 | #10178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13079554 | 2 |
| C2×#10622628 | 2 |
| #13067285 | 2 |
| #13067019 | 2 |
| #13066937 | 2 |
| #13066511 | 2 |
| C11×#3077 | 2 |
| #10178 | 11 |