Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
954 conjugacy classes of subgroups; only the 268 normal subgroups are shown.
This group has 954 conjugacy classes of subgroups — too many to draw. Only its 268 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 |
|---|---|---|
| 9. #11719057 | C4 | semidirect |
| 10. C42×#261 | C4 | semidirect |
| 11. C2×C4×C8×C13 | C4 | semidirect |
| 12. C2×#88055 | C4 | semidirect |
| 13. C2×C4×#1055 | C4 | semidirect |
| 15. #11718267 | C4 | direct (N × H) |
| 57. C4×#261 | C42 | semidirect |
| 60. C2×C8×C13 | C42 | semidirect |
| 70. C2×#1055 | C42 | semidirect |
| 105. C2×C4×C8 | #261 | semidirect |
| 119. C4×C13 | H(3,ℤ/4) | semidirect |
| 171. C2×C8 | C4×#261 | semidirect |
| 184. C13 | C4×H(3,ℤ/4) | semidirect |
| 219. C4 | #11718267 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#88237 | 2 |
| C2×#11718267 | 2 |
| C2×C4×#6094 | 2 |
| C4×H(3,ℤ/4) | 13 |