Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
702 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 702 conjugacy classes of subgroups — too many to draw. Only its 195 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 |
|---|---|---|
| 3. #13116924 | C2 | direct (N × H) |
| 4. C2×#11718096 | C2 | semidirect |
| 5. C2×#11718156 | C2 | semidirect |
| 6. C22×C13×Q32 | C2 | semidirect |
| 11. C2×C13×Q32 | C22 | semidirect |
| 20. #11718156 | C22 | semidirect |
| 21. #11718096 | C22 | semidirect |
| 80. C22×Q32 | D13 | semidirect |
| 89. C22×D13 | Q32 | semidirect |
| 115. C2×Q32 | C2×D13 | semidirect |
| 133. C2×D13 | C2×Q32 | semidirect |
| 166. C2×C13 | #2216 | semidirect |
| 202. C13 | C2×#2216 | semidirect |
| 243. C2 | #13116924 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C16×D13 | 2 |
| C2×#11718849 | 2 |
| #13116924 | 2 |
| C2×#11718096 | 2 |
| C2×#11718156 | 2 |
| C22×C13×Q32 | 2 |
| C2×#2216 | 13 |