Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
3350 conjugacy classes of subgroups; only the 827 normal subgroups are shown.
This group has 3350 conjugacy classes of subgroups — too many to draw. Only its 827 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. C23×#6107 | C2 | semidirect |
| 4. C2×#11718747 | C2 | direct (N × H) |
| 5. C22×#88043 | C2 | semidirect |
| 6. C22×C13×C4⋊Q8 | C2 | semidirect |
| 11. C2×C13×C4⋊Q8 | C22 | semidirect |
| 15. C22×#6107 | C22 | semidirect |
| 22. #11718747 | C22 | direct (N × H) |
| 23. C2×#88043 | C22 | semidirect |
| 40. C13×C4⋊Q8 | C23 | semidirect |
| 45. C2×#6107 | C23 | semidirect |
| 53. #88043 | C23 | semidirect |
| 91. C22×C4⋊Q8 | D13 | semidirect |
| 129. C2×C4⋊Q8 | C2×D13 | semidirect |
| 137. C22×C13 | #497 | semidirect |
| 171. C4⋊Q8 | C22×D13 | semidirect |
| 179. C2×C13 | C2×#497 | semidirect |
| 217. C13 | C22×#497 | semidirect |
| 246. C22 | #11718747 | direct (N × H) |
| 256. C2 | C2×#11718747 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#6107 | 2 |
| C23×#6106 | 2 |
| C22×#88129 | 2 |
| C2×#11718747 | 2 |
| C22×#88043 | 2 |
| C22×C13×C4⋊Q8 | 2 |
| C22×#497 | 13 |