Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
242 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 86 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. #13131220 | C2 | semidirect |
| 2. D4×#6092 | C2 | semidirect |
| 3. #13129858 | C2 | semidirect |
| 4. D4⋊#6092 | C2 | semidirect |
| 5. D4⋊#6092 | C2 | semidirect |
| 6. #13129751 | C2 | semidirect |
| 84. D4×C13 | M32 | semidirect |
| 184. C13 | #12063 | semidirect |
| 190. D4 | #88106 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13131220 | 2 |
| D4×#6092 | 2 |
| #13129858 | 2 |
| D4⋊#6092 | 2 |
| #13129751 | 2 |
| D8×#1055 | 2 |
| #12063 | 13 |