Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
238 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 74 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. Q16×#1057 | C2 | semidirect |
| 3. #13129868 | C2 | semidirect |
| 4. #13129792 | C2 | semidirect |
| 6. #13129747 | C2 | semidirect |
| 39. #88068 | C8 | semidirect |
| 55. C13×Q16 | C2×C8 | semidirect |
| 68. #6090 | C2×C8 | semidirect |
| 153. Q16 | D13⋊C8 | semidirect |
| 173. C13 | #12043 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×#1057 | 2 |
| #13130417 | 2 |
| #13129868 | 2 |
| #13129792 | 2 |
| #13129791 | 2 |
| #13129747 | 2 |
| #13116685 | 2 |
| #12043 | 13 |