Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
43678 conjugacy classes of subgroups; only the 13003 normal subgroups are shown.
This group has 43678 conjugacy classes of subgroups — too many to draw. Only its 13003 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. C25×Dic13 | C2 | semidirect |
| 2. C23×C22⋊Dic13 | C2 | direct (N × H) |
| 5. C26×C13 | C4 | semidirect |
| 9. C24×Dic13 | C22 | semidirect |
| 10. C22×C22⋊Dic13 | C22 | direct (N × H) |
| 14. C25×C13 | C2×C4 | semidirect |
| 19. C23×Dic13 | C23 | semidirect |
| 20. C2×C22⋊Dic13 | C23 | direct (N × H) |
| 24. C24×C13 | C22⋊C4 | semidirect |
| 26. C24×C13 | C22×C4 | semidirect |
| 31. C22×Dic13 | C24 | semidirect |
| 32. C22⋊Dic13 | C24 | direct (N × H) |
| 38. C23×C13 | C2×C22⋊C4 | semidirect |
| 40. C23×C13 | C23×C4 | semidirect |
| 45. C2×Dic13 | C25 | semidirect |
| 47. C26 | Dic13 | semidirect |
| 55. C22×C13 | C22×C22⋊C4 | semidirect |
| 57. C22×C13 | C24×C4 | semidirect |
| 64. C25 | C2×Dic13 | semidirect |
| 72. C2×C13 | C23×C22⋊C4 | semidirect |
| 77. C24 | C22⋊Dic13 | direct (N × H) |
| 79. C24 | C22×Dic13 | semidirect |
| 86. C13 | C24×C22⋊C4 | semidirect |
| 89. C23 | C2×C22⋊Dic13 | direct (N × H) |
| 91. C23 | C23×Dic13 | semidirect |
| 99. C22 | C22×C22⋊Dic13 | direct (N × H) |
| 101. C22 | C24×Dic13 | semidirect |
| 106. C2 | C23×C22⋊Dic13 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×Dic13 | 2 |
| C23×C22⋊Dic13 | 2 |
| C27×C13 | 2 |
| C24×C22⋊C4 | 13 |