Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
214 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 56 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. D16×#261 | C2 | semidirect |
| 2. #13129997 | C2 | semidirect |
| 3. #13129985 | C2 | semidirect |
| 4. C32×#261 | C2 | semidirect |
| 12. C13×D32 | C4 | semidirect |
| 13. #11718111 | C4 | semidirect |
| 14. D416 | C4 | semidirect |
| 22. C13×D16 | C2×C4 | semidirect |
| 24. D208 | C2×C4 | semidirect |
| 27. C13×C32 | C2×C4 | semidirect |
| 28. #88034 | C2×C4 | semidirect |
| 64. D32 | #261 | direct (N × H) |
| 77. #261 | D32 | direct (N × H) |
| 84. D16 | C2×#261 | semidirect |
| 92. C32 | C2×#261 | semidirect |
| 111. C13 | C4×D32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D16×#261 | 2 |
| #13129997 | 2 |
| #13129985 | 2 |
| C32×#261 | 2 |
| D13×D32 | 2 |
| C4×D32 | 13 |