Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
252 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 252 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. #13131215 | C2 | semidirect |
| 2. D4×#6092 | C2 | semidirect |
| 3. #13129859 | C2 | semidirect |
| 4. #13129787 | C2 | semidirect |
| 5. D4⋊#6092 | C2 | semidirect |
| 6. #13129751 | C2 | semidirect |
| 55. #6104 | C16 | semidirect |
| 82. D4×C13 | C2×C16 | semidirect |
| 91. D52 | C2×C16 | semidirect |
| 99. #1055 | C2×C16 | semidirect |
| 184. C13 | #12062 | semidirect |
| 190. D4 | D13⋊C16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13131215 | 2 |
| D4×#6092 | 2 |
| #13129859 | 2 |
| #13129787 | 2 |
| D4⋊#6092 | 2 |
| #13129751 | 2 |
| #13113628 | 2 |
| #12062 | 13 |