Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
3774 conjugacy classes of subgroups; only the 1579 normal subgroups are shown.
This group has 3774 conjugacy classes of subgroups — too many to draw. Only its 1579 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. #13123234 | C2 | direct (N × H) |
| 19. C2×C42×C13 | Q8 | semidirect |
| 37. C42×C13 | C2×Q8 | semidirect |
| 47. C2×C4×C13 | C4⋊Q8 | semidirect |
| 67. C4×C13 | C2×C4⋊Q8 | semidirect |
| 77. C2×C42 | Dic26 | semidirect |
| 81. C2×C13 | #2868 | semidirect |
| 95. C42 | C2×Dic26 | semidirect |
| 97. C13 | C2×#2868 | semidirect |
| 104. C2×C4 | #88123 | semidirect |
| 114. C4 | C2×#88123 | semidirect |
| 116. C2 | #13123234 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#88123 | 2 |
| #13123234 | 2 |
| C2×#11718596 | 2 |
| C2×C43×C13 | 2 |
| C2×#2868 | 13 |