Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
516 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 2. #13123687 | C2 | semidirect |
| 3. C2×#11718087 | C2 | semidirect |
| 4. #13116551 | C2 | semidirect |
| 5. #13115744 | C2 | semidirect |
| 6. #13112924 | C2 | semidirect |
| 7. C13×#1382 | C2 | semidirect |
| 21. C2×D208 | C4 | semidirect |
| 42. C2×D104 | C2×C4 | semidirect |
| 50. C2×C13×C16 | C2×C4 | semidirect |
| 115. #1382 | D13 | semidirect |
| 213. C2×C16 | C4×D13 | semidirect |
| 274. C13 | #13017 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D208 | 2 |
| #13123687 | 2 |
| C2×#11718087 | 2 |
| #13116551 | 2 |
| #13115744 | 2 |
| #13112924 | 2 |
| C13×#1382 | 2 |
| #13017 | 13 |