Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
840 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 107 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×#11718067 | C2 | semidirect |
| 3. #13114824 | C2 | semidirect |
| 4. C4×C13×#100 | C2 | semidirect |
| 5. C23×D52 | C4 | semidirect |
| 13. #11718873 | C4 | semidirect |
| 16. #11718616 | C4 | semidirect |
| 49. C13×#100 | D4 | semidirect |
| 113. C4×#100 | D13 | semidirect |
| 216. C4×C13 | AΣL(1,𝔽16) | semidirect |
| 247. #100 | D52 | semidirect |
| 316. C13 | #13218 | semidirect |
| 405. C4 | #11718067 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13118192 | 2 |
| C2×#11718067 | 2 |
| #13114824 | 2 |
| C4×C13×#100 | 2 |
| #13218 | 13 |