Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
2334 conjugacy classes of subgroups; only the 1464 normal subgroups are shown.
This group has 2334 conjugacy classes of subgroups — too many to draw. Only its 1464 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. C22×#88106 | C2 | direct (N × H) |
| 2. C23×#6092 | C2 | semidirect |
| 9. C2×#88106 | C22 | direct (N × H) |
| 10. C22×#6092 | C22 | semidirect |
| 21. #88106 | C23 | direct (N × H) |
| 22. C2×#6092 | C23 | semidirect |
| 37. #6092 | C24 | semidirect |
| 42. C23×C13 | M32 | semidirect |
| 61. C22×C13 | C2×M32 | semidirect |
| 80. C2×C13 | C22×M32 | semidirect |
| 96. C13 | C23×M32 | semidirect |
| 98. C23 | #88106 | direct (N × H) |
| 110. C22 | C2×#88106 | direct (N × H) |
| 117. C2 | C22×#88106 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#88106 | 2 |
| C23×#6092 | 2 |
| C24×#1055 | 2 |
| C23×M32 | 13 |