Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
270 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 171 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 |
|---|---|---|
| 3. C4×#88034 | C2 | semidirect |
| 4. C32×Dic13 | C2 | semidirect |
| 5. C4×C13×C32 | C2 | semidirect |
| 15. D13×C32 | C4 | direct (N × H) |
| 29. C13×C32 | C2×C4 | semidirect |
| 30. #88034 | C2×C4 | semidirect |
| 52. C4×C32 | D13 | direct (N × H) |
| 58. C4×D13 | C32 | direct (N × H) |
| 79. C4×C13 | C2×C32 | semidirect |
| 83. Dic13 | C2×C32 | semidirect |
| 98. C32 | C4×D13 | direct (N × H) |
| 101. D13 | C4×C32 | direct (N × H) |
| 118. C13 | C2×C4×C32 | semidirect |
| 137. C4 | D13×C32 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D13×C32 | 2 |
| C4×C16×D13 | 2 |
| C4×#88034 | 2 |
| C32×Dic13 | 2 |
| C4×C13×C32 | 2 |
| C2×C4×C32 | 13 |