Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
238 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 88 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. Q8×#6092 | C2 | semidirect |
| 3. #13129859 | C2 | semidirect |
| 4. Q8⋊#6092 | C2 | semidirect |
| 6. C8×#6092 | C2 | semidirect |
| 54. #6106 | C16 | semidirect |
| 68. #6092 | SD16 | semidirect |
| 78. Q8×C13 | C2×C16 | semidirect |
| 94. #1055 | C2×C16 | semidirect |
| 173. C13 | C16×SD16 | semidirect |
| 176. Q8 | D13⋊C16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#6092 | 2 |
| #13131215 | 2 |
| #13129859 | 2 |
| Q8⋊#6092 | 2 |
| #13129787 | 2 |
| C8×#6092 | 2 |
| #13113633 | 2 |
| C16×SD16 | 13 |