Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
860 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 860 conjugacy classes of subgroups — too many to draw. Only its 127 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. #13116508 | C2 | semidirect |
| 2. #13116501 | C2 | semidirect |
| 3. #13115364 | C2 | semidirect |
| 4. #13115220 | C2 | semidirect |
| 7. C13×H(3,𝔽4) | C4 | semidirect |
| 9. C13×#555 | C4 | semidirect |
| 17. #11719524 | C22 | semidirect |
| 18. #11718901 | C22 | semidirect |
| 19. #11718901 | C22 | semidirect |
| 187. H(3,𝔽4) | Dic13 | semidirect |
| 189. #555 | Dic13 | semidirect |
| 343. C13 | #12778 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13116508 | 2 |
| #13116501 | 2 |
| #13115364 | 2 |
| #13115220 | 2 |
| C13×#3549 | 2 |
| #12778 | 13 |