Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
542 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 156 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 |
|---|---|---|
| 3. M16×#1057 | C2 | semidirect |
| 4. #13129682 | C2 | semidirect |
| 43. C13×#100 | C8 | semidirect |
| 44. #88073 | C8 | semidirect |
| 72. C13×M16 | C2×C8 | semidirect |
| 79. #6099 | C2×C8 | semidirect |
| 113. #1057 | #100 | direct (N × H) |
| 166. #100 | #1057 | direct (N × H) |
| 196. M16 | C2×#1057 | semidirect |
| 213. C13 | C8×#100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#1057 | 2 |
| #13130076 | 2 |
| M16×#1057 | 2 |
| #13129682 | 2 |
| #100×Dic13 | 2 |
| C8×#100 | 13 |