Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
462 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 139 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. C2×Dic208 | C2 | semidirect |
| 3. C2×#11718114 | C2 | semidirect |
| 4. D13×Q64 | C2 | direct (N × H) |
| 6. C2×C13×Q64 | C2 | semidirect |
| 14. C13×Q64 | C22 | semidirect |
| 16. #11718114 | C22 | semidirect |
| 18. Dic208 | C22 | semidirect |
| 62. C2×Q64 | D13 | direct (N × H) |
| 89. Q64 | C2×D13 | direct (N × H) |
| 94. C2×D13 | Q64 | direct (N × H) |
| 119. C2×C13 | C2×Q64 | semidirect |
| 121. D13 | C2×Q64 | direct (N × H) |
| 141. C13 | C22×Q64 | semidirect |
| 167. C2 | D13×Q64 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D13×Q32 | 2 |
| C2×Dic208 | 2 |
| C2×#11718114 | 2 |
| D13×Q64 | 2 |
| C2×D13×C32 | 2 |
| C2×C13×Q64 | 2 |
| C22×Q64 | 13 |