Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
3550 conjugacy classes of subgroups; only the 667 normal subgroups are shown.
This group has 3550 conjugacy classes of subgroups — too many to draw. Only its 667 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. #13123089 | C2 | direct (N × H) |
| 2. C2×#11718608 | C2 | semidirect |
| 6. C23×Dic26 | C22 | semidirect |
| 11. C2×#88071 | C22 | semidirect |
| 12. #11718608 | C22 | semidirect |
| 14. C25×C13 | Q8 | semidirect |
| 20. C22×Dic26 | C23 | semidirect |
| 25. #88071 | C23 | semidirect |
| 33. C24×C13 | C2×Q8 | semidirect |
| 85. C25 | Dic26 | semidirect |
| 98. C2×C13 | #2840 | semidirect |
| 107. C24 | C2×Dic26 | semidirect |
| 118. C13 | C2×#2840 | semidirect |
| 148. C2 | #13123089 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13123089 | 2 |
| C2×#11718608 | 2 |
| C2×#11718908 | 2 |
| C2×C13×#379 | 2 |
| C2×#2840 | 13 |