Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
11422 conjugacy classes of subgroups; only the 5752 normal subgroups are shown.
This group has 11422 conjugacy classes of subgroups — too many to draw. Only its 5752 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×#88240 | C2 | direct (N × H) |
| 2. C23×#6118 | C2 | semidirect |
| 3. C23×D13⋊C8 | C2 | semidirect |
| 12. C2×#88240 | C22 | direct (N × H) |
| 13. C22×#6118 | C22 | semidirect |
| 14. C22×D13⋊C8 | C22 | semidirect |
| 26. #88240 | C23 | direct (N × H) |
| 27. C2×#6118 | C23 | semidirect |
| 28. C2×D13⋊C8 | C23 | semidirect |
| 44. #6118 | C24 | semidirect |
| 45. D13⋊C8 | C24 | semidirect |
| 50. C23×C13 | #131 | semidirect |
| 73. C22×C13 | C2×#131 | semidirect |
| 94. C2×C13 | C22×#131 | semidirect |
| 113. C13 | C23×#131 | semidirect |
| 116. C23 | #88240 | direct (N × H) |
| 129. C22 | C2×#88240 | direct (N × H) |
| 135. C2 | C22×#88240 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#88240 | 2 |
| C23×#6118 | 2 |
| C23×D13⋊C8 | 2 |
| C23×#6131 | 2 |
| C23×#131 | 13 |