Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
238 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 82 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. Q16×#1057 | C2 | semidirect |
| 3. #13129867 | C2 | semidirect |
| 4. #13129792 | C2 | semidirect |
| 6. #13129747 | C2 | semidirect |
| 36. C13×SD32 | C8 | semidirect |
| 55. C13×Q16 | C2×C8 | semidirect |
| 67. C13×C16 | C2×C8 | semidirect |
| 129. SD32 | #1057 | semidirect |
| 153. Q16 | C2×#1057 | semidirect |
| 172. C16 | C2×#1057 | semidirect |
| 173. C13 | #12043 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×#1057 | 2 |
| D8×#1057 | 2 |
| #13129867 | 2 |
| #13129792 | 2 |
| #13129790 | 2 |
| #13129747 | 2 |
| SD32×Dic13 | 2 |
| #12043 | 13 |