Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
2334 conjugacy classes of subgroups; only the 747 normal subgroups are shown.
This group has 2334 conjugacy classes of subgroups — too many to draw. Only its 747 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×Dic52 | C2 | semidirect |
| 3. C22×#88040 | C2 | direct (N × H) |
| 4. C23×C13×C16 | C2 | semidirect |
| 9. C22×Dic52 | C22 | semidirect |
| 12. C22×C13×C16 | C22 | semidirect |
| 13. C2×#88040 | C22 | direct (N × H) |
| 24. C2×Dic52 | C23 | semidirect |
| 27. C2×C13×C16 | C23 | semidirect |
| 28. #88040 | C23 | direct (N × H) |
| 43. Dic52 | C24 | semidirect |
| 46. C13×C16 | C24 | semidirect |
| 50. C23×C16 | D13 | semidirect |
| 51. C23×C13 | SD32 | semidirect |
| 72. C22×C16 | C2×D13 | semidirect |
| 73. C22×C13 | C2×SD32 | semidirect |
| 94. C2×C16 | C22×D13 | semidirect |
| 95. C2×C13 | C22×SD32 | semidirect |
| 114. C16 | C23×D13 | semidirect |
| 115. C13 | C23×SD32 | semidirect |
| 118. C23 | #88040 | direct (N × H) |
| 131. C22 | C2×#88040 | direct (N × H) |
| 137. C2 | C22×#88040 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic52 | 2 |
| C23×D104 | 2 |
| C22×#88040 | 2 |
| C23×C13×C16 | 2 |
| C23×SD32 | 13 |