Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
13310 conjugacy classes of subgroups; only the 6264 normal subgroups are shown.
This group has 13310 conjugacy classes of subgroups — too many to draw. Only its 6264 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. C23×#6122 | C2 | direct (N × H) |
| 2. C24×#1057 | C2 | semidirect |
| 9. C22×#6122 | C22 | direct (N × H) |
| 10. C23×#1057 | C22 | semidirect |
| 19. C2×#6122 | C23 | direct (N × H) |
| 20. C22×#1057 | C23 | semidirect |
| 23. C24×C13 | M16 | semidirect |
| 31. #6122 | C24 | direct (N × H) |
| 32. C2×#1057 | C24 | semidirect |
| 37. C23×C13 | C2×M16 | semidirect |
| 45. #1057 | C25 | semidirect |
| 54. C22×C13 | C22×M16 | semidirect |
| 71. C2×C13 | C23×M16 | semidirect |
| 74. C24 | #6122 | direct (N × H) |
| 84. C13 | C24×M16 | semidirect |
| 86. C23 | C2×#6122 | direct (N × H) |
| 96. C22 | C22×#6122 | direct (N × H) |
| 103. C2 | C23×#6122 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#6122 | 2 |
| C24×#1057 | 2 |
| C25×Dic13 | 2 |
| C24×M16 | 13 |