Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
840 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 111 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×#11718128 | C2 | semidirect |
| 2. #13114824 | C2 | semidirect |
| 3. C4×#88073 | C2 | semidirect |
| 5. C23×D4×C13 | C4 | semidirect |
| 12. C13×#380 | C4 | semidirect |
| 13. C13×#379 | C4 | semidirect |
| 51. #88073 | D4 | semidirect |
| 169. C23×D4 | Dic13 | semidirect |
| 180. #380 | Dic13 | semidirect |
| 181. #379 | Dic13 | semidirect |
| 217. C4×C13 | AΣL(1,𝔽16) | semidirect |
| 316. C13 | #13218 | semidirect |
| 405. C4 | #11718128 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11718128 | 2 |
| #13114824 | 2 |
| C4×#88073 | 2 |
| C13×#2408 | 2 |
| #13218 | 13 |