Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
664 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 664 conjugacy classes of subgroups — too many to draw. Only its 159 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×D13×Q32 | C2 | semidirect |
| 3. #13117089 | C2 | semidirect |
| 4. #13116928 | C2 | semidirect |
| 5. #13116886 | C2 | semidirect |
| 6. #13116771 | C2 | semidirect |
| 8. C4×C13×Q32 | C2 | semidirect |
| 44. C13×Q32 | D4 | semidirect |
| 97. C4×Q32 | D13 | semidirect |
| 109. D52 | Q32 | direct (N × H) |
| 143. C2×D13 | C2×Q32 | semidirect |
| 147. C4×C13 | C2×Q32 | semidirect |
| 170. Q32 | D52 | direct (N × H) |
| 217. C13 | D4×Q32 | semidirect |
| 248. C4 | D13×Q32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D13×Q32 | 2 |
| Q16×D52 | 2 |
| #13117089 | 2 |
| #13116928 | 2 |
| #13116886 | 2 |
| #13116771 | 2 |
| C16×D52 | 2 |
| C4×C13×Q32 | 2 |
| D4×Q32 | 13 |