Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
334 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 128 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 |
|---|---|---|
| 14. C4×C13×C16 | C4 | semidirect |
| 15. #11718094 | C4 | semidirect |
| 16. C4×#6090 | C4 | semidirect |
| 57. C13×C16 | C4⋊C4 | semidirect |
| 58. #6090 | C4⋊C4 | semidirect |
| 91. C4×C16 | #261 | semidirect |
| 97. C4×C13 | #365 | semidirect |
| 147. C16 | C4⋊#261 | semidirect |
| 148. C13 | #12903 | semidirect |
| 174. C4 | #11718219 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11718219 | 2 |
| #13130775 | 2 |
| #13130771 | 2 |
| C4×#88038 | 2 |
| #12903 | 13 |