Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
866 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 866 conjugacy classes of subgroups — too many to draw. Only its 251 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×#11718742 | C2 | semidirect |
| 4. #13114438 | C2 | direct (N × H) |
| 5. C2×C8×#1055 | C2 | semidirect |
| 6. C2×C13×#498 | C2 | semidirect |
| 12. C13×#498 | C22 | semidirect |
| 19. #11718742 | C22 | semidirect |
| 24. C8×#1055 | C22 | semidirect |
| 86. C2×#498 | D13 | semidirect |
| 121. #498 | C2×D13 | semidirect |
| 175. C2×C13 | #1708 | semidirect |
| 210. C13 | C2×#1708 | semidirect |
| 248. C2 | #13114438 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11718354 | 2 |
| C2×#11718742 | 2 |
| C2×#11718749 | 2 |
| #13114438 | 2 |
| C2×C8×#1055 | 2 |
| C2×C13×#498 | 2 |
| C2×#1708 | 13 |