Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
14334 conjugacy classes of subgroups; only the 4427 normal subgroups are shown.
This group has 14334 conjugacy classes of subgroups — too many to draw. Only its 4427 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 |
|---|---|---|
| 2. C22×#88201 | C2 | direct (N × H) |
| 3. C23×#6103 | C2 | semidirect |
| 4. C23×C4×Dic13 | C2 | semidirect |
| 5. C24×Q8×C13 | C2 | semidirect |
| 8. C23×Q8×C13 | C22 | semidirect |
| 14. C2×#88201 | C22 | direct (N × H) |
| 15. C22×#6103 | C22 | semidirect |
| 16. C22×C4×Dic13 | C22 | semidirect |
| 22. C22×Q8×C13 | C23 | semidirect |
| 31. #88201 | C23 | direct (N × H) |
| 32. C2×#6103 | C23 | semidirect |
| 33. C2×C4×Dic13 | C23 | semidirect |
| 43. C2×Q8×C13 | C24 | semidirect |
| 52. #6103 | C24 | semidirect |
| 53. C4×Dic13 | C24 | semidirect |
| 54. C24×Q8 | D13 | semidirect |
| 59. C23×C13 | #124 | semidirect |
| 77. C23×Q8 | C2×D13 | semidirect |
| 86. C22×C13 | C2×#124 | semidirect |
| 101. C22×Q8 | C22×D13 | semidirect |
| 113. C2×C13 | C22×#124 | semidirect |
| 125. C2×Q8 | C23×D13 | semidirect |
| 136. C13 | C23×#124 | semidirect |
| 141. C23 | #88201 | direct (N × H) |
| 156. C22 | C2×#88201 | direct (N × H) |
| 164. C2 | C22×#88201 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×D52 | 2 |
| C22×#88201 | 2 |
| C23×#6103 | 2 |
| C23×C4×Dic13 | 2 |
| C24×Q8×C13 | 2 |
| C23×#124 | 13 |