Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
732 conjugacy classes of subgroups; only the 243 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 243 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. #13115391 | C2 | semidirect |
| 4. #13114707 | C2 | semidirect |
| 6. C42×#1055 | C2 | semidirect |
| 7. C13×#1839 | C2 | semidirect |
| 66. C42×C13 | M16 | semidirect |
| 81. #1839 | D13 | semidirect |
| 109. #1055 | #126 | semidirect |
| 195. C42 | #6094 | semidirect |
| 196. C13 | #21666 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#88130 | 2 |
| #13115440 | 2 |
| #13115391 | 2 |
| #13114707 | 2 |
| #13114616 | 2 |
| C42×#1055 | 2 |
| C13×#1839 | 2 |
| #21666 | 13 |