Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
720 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 720 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. C4×#88074 | C2 | semidirect |
| 3. #13112961 | C2 | semidirect |
| 7. C2×C4×D4×C13 | C4 | semidirect |
| 10. C13×#390 | C4 | semidirect |
| 12. C13×#384 | C4 | semidirect |
| 13. C43×C13 | C4 | semidirect |
| 16. #11718137 | C4 | direct (N × H) |
| 45. #88074 | C2×C4 | semidirect |
| 58. C2×D4×C13 | C42 | semidirect |
| 88. C42×C13 | C42 | semidirect |
| 140. C2×C4×D4 | Dic13 | semidirect |
| 144. #390 | Dic13 | semidirect |
| 146. #384 | Dic13 | semidirect |
| 148. C43 | Dic13 | semidirect |
| 174. C4×C13 | #353 | semidirect |
| 222. C2×D4 | C4×Dic13 | semidirect |
| 255. C42 | C4×Dic13 | semidirect |
| 256. C13 | C4×#353 | semidirect |
| 323. C4 | #11718137 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11718137 | 2 |
| C4×#88074 | 2 |
| #13112961 | 2 |
| C4×C13×#127 | 2 |
| C4×#353 | 13 |