Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
9486 conjugacy classes of subgroups; only the 3915 normal subgroups are shown.
This group has 9486 conjugacy classes of subgroups — too many to draw. Only its 3915 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×#88130 | C2 | direct (N × H) |
| 2. C23×#6101 | C2 | semidirect |
| 4. C23×C42×C13 | C2 | semidirect |
| 8. C22×C42×C13 | C22 | semidirect |
| 10. C22×#6101 | C22 | semidirect |
| 11. C2×#88130 | C22 | direct (N × H) |
| 19. C2×C42×C13 | C23 | semidirect |
| 21. C2×#6101 | C23 | semidirect |
| 22. #88130 | C23 | direct (N × H) |
| 33. C42×C13 | C24 | semidirect |
| 35. #6101 | C24 | semidirect |
| 39. C23×C42 | D13 | semidirect |
| 40. C23×C13 | #126 | semidirect |
| 56. C22×C42 | C2×D13 | semidirect |
| 57. C22×C13 | C2×#126 | semidirect |
| 74. C2×C42 | C22×D13 | semidirect |
| 75. C2×C13 | C22×#126 | semidirect |
| 89. C42 | C23×D13 | semidirect |
| 90. C13 | C23×#126 | semidirect |
| 94. C23 | #88130 | direct (N × H) |
| 103. C22 | C2×#88130 | direct (N × H) |
| 109. C2 | C22×#88130 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#88130 | 2 |
| C23×#6101 | 2 |
| C23×#6103 | 2 |
| C23×C42×C13 | 2 |
| C23×#126 | 13 |