Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
1708 conjugacy classes of subgroups; only the 288 normal subgroups are shown.
This group has 1708 conjugacy classes of subgroups — too many to draw. Only its 288 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. C24×#1057 | C2 | semidirect |
| 2. C2×#11719144 | C2 | semidirect |
| 3. #13130809 | C2 | semidirect |
| 4. #13130780 | C2 | semidirect |
| 5. #13130658 | C2 | semidirect |
| 6. #13130573 | C2 | semidirect |
| 9. C22×#6122 | C22 | semidirect |
| 17. C2×C22⋊#1057 | C22 | semidirect |
| 19. C2×#88112 | C22 | semidirect |
| 20. C2×#88110 | C22 | semidirect |
| 25. #11718290 | C22 | semidirect |
| 38. C22×#1057 | D4 | semidirect |
| 61. C24×C13 | M16 | semidirect |
| 137. #1057 | #120 | semidirect |
| 164. C22×C13 | #435 | semidirect |
| 213. C24 | #6122 | semidirect |
| 250. C13 | #21440 | semidirect |
| 292. C22 | #11719144 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×#1057 | 2 |
| C2×#11719144 | 2 |
| #13130809 | 2 |
| #13130780 | 2 |
| #13130658 | 2 |
| #13130573 | 2 |
| #120×Dic13 | 2 |
| #21440 | 13 |