Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
338 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 79 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. #13117061 | C2 | semidirect |
| 3. #13114196 | C2 | semidirect |
| 4. #13112891 | C2 | semidirect |
| 5. Q8⋊#6090 | C2 | semidirect |
| 6. #13112797 | C2 | semidirect |
| 7. Q8×C13×D8 | C2 | semidirect |
| 66. C13×D8 | SD16 | semidirect |
| 87. Q8×D8 | D13 | semidirect |
| 100. Q8×C13 | D16 | semidirect |
| 205. D8 | #6106 | semidirect |
| 222. C13 | #12352 | semidirect |
| 229. Q8 | #88066 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13117061 | 2 |
| #13116871 | 2 |
| #13114196 | 2 |
| #13112891 | 2 |
| Q8⋊#6090 | 2 |
| #13112797 | 2 |
| Q8×C13×D8 | 2 |
| #12352 | 13 |