Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
240 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 83 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. #13113721 | C2 | semidirect |
| 2. D8×#1055 | C2 | semidirect |
| 3. #13112910 | C2 | semidirect |
| 4. #13112797 | C2 | semidirect |
| 5. #13112797 | C2 | semidirect |
| 6. #13112755 | C2 | semidirect |
| 52. C13×D8 | M16 | semidirect |
| 162. D8 | #6099 | semidirect |
| 180. C13 | #12073 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13113721 | 2 |
| D8×#1055 | 2 |
| #13112910 | 2 |
| #13112797 | 2 |
| #13112755 | 2 |
| C4×C13×D16 | 2 |
| #12073 | 13 |