Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
562 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 562 conjugacy classes of subgroups — too many to draw. Only its 167 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. #13127811 | C2 | semidirect |
| 2. #13117061 | C2 | semidirect |
| 3. #13116970 | C2 | semidirect |
| 4. #13116871 | C2 | semidirect |
| 5. Q8×#6090 | C2 | semidirect |
| 6. C4×#88066 | C2 | semidirect |
| 7. Q8×C13×D8 | C2 | semidirect |
| 58. C13×D8 | #41 | semidirect |
| 74. Q8×D8 | D13 | semidirect |
| 83. Q8×C13 | D16 | semidirect |
| 170. D8 | #6131 | semidirect |
| 182. C13 | #33925 | semidirect |
| 186. Q8 | #88066 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13127811 | 2 |
| #13117061 | 2 |
| #13116970 | 2 |
| #13116871 | 2 |
| Q8×#6090 | 2 |
| C4×#88066 | 2 |
| Q8×C13×D8 | 2 |
| #33925 | 13 |