Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
238 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 3. #13112899 | C2 | semidirect |
| 4. Q8⋊#6090 | C2 | semidirect |
| 6. C16×#1055 | C2 | semidirect |
| 7. Q8×C13×C16 | C2 | semidirect |
| 55. #6106 | C16 | direct (N × H) |
| 66. C13×C16 | SD16 | semidirect |
| 69. Q8×C16 | D13 | semidirect |
| 78. Q8×C13 | C2×C16 | semidirect |
| 96. #1055 | C2×C16 | semidirect |
| 172. C16 | #6106 | direct (N × H) |
| 173. C13 | C16×SD16 | semidirect |
| 176. Q8 | C16×D13 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C16×D52 | 2 |
| C8×#6106 | 2 |
| #13112899 | 2 |
| Q8⋊#6090 | 2 |
| #13112790 | 2 |
| C16×#1055 | 2 |
| Q8×C13×C16 | 2 |
| C16×SD16 | 13 |