Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
274 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 69 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. #13116876 | C2 | semidirect |
| 3. Q16×#1055 | C2 | semidirect |
| 4. #13112905 | C2 | semidirect |
| 5. #13112883 | C2 | semidirect |
| 6. #13112882 | C2 | semidirect |
| 7. C13×#2207 | C2 | semidirect |
| 55. C13×Q16 | D8 | semidirect |
| 78. #2207 | D13 | semidirect |
| 109. #1055 | SD32 | semidirect |
| 175. Q16 | #6104 | semidirect |
| 197. C13 | #12425 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13116876 | 2 |
| #13114450 | 2 |
| Q16×#1055 | 2 |
| #13112905 | 2 |
| #13112883 | 2 |
| #13112882 | 2 |
| C13×#2207 | 2 |
| #12425 | 13 |