Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
542 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 144 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. #88063 | C8 | semidirect |
| 71. C13×M16 | C2×C8 | semidirect |
| 78. #6099 | C2×C8 | semidirect |
| 112. #1057 | #100 | semidirect |
| 194. M16 | D13⋊C8 | semidirect |
| 211. C13 | C8×#100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11719073 | 2 |
| #13130077 | 2 |
| M16×#1057 | 2 |
| #13129682 | 2 |
| #13114627 | 2 |
| C8×#100 | 13 |