Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
3614 conjugacy classes of subgroups; only the 1464 normal subgroups are shown.
This group has 3614 conjugacy classes of subgroups — too many to draw. Only its 1464 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×#88101 | C2 | direct (N × H) |
| 8. C23×C8×C13 | C4 | semidirect |
| 9. C23×#1055 | C4 | semidirect |
| 10. C22×C8×D13 | C4 | semidirect |
| 12. C2×#88101 | C22 | direct (N × H) |
| 24. C22×C8×C13 | C2×C4 | semidirect |
| 25. C22×#1055 | C2×C4 | semidirect |
| 26. C2×C8×D13 | C2×C4 | semidirect |
| 28. #88101 | C23 | direct (N × H) |
| 47. C2×C8×C13 | C22×C4 | semidirect |
| 48. C2×#1055 | C22×C4 | semidirect |
| 49. C8×D13 | C22×C4 | semidirect |
| 54. C23×C13 | #106 | semidirect |
| 56. C22×D13 | #106 | semidirect |
| 71. C8×C13 | C23×C4 | semidirect |
| 72. #1055 | C23×C4 | semidirect |
| 78. C23×C8 | #261 | semidirect |
| 82. C22×C13 | C2×#106 | semidirect |
| 84. C2×D13 | C2×#106 | semidirect |
| 105. C22×C8 | C2×#261 | semidirect |
| 109. C2×C13 | C22×#106 | semidirect |
| 111. D13 | C22×#106 | semidirect |
| 131. C2×C8 | C22×#261 | semidirect |
| 134. C13 | C23×#106 | semidirect |
| 139. C23 | #88101 | direct (N × H) |
| 153. C8 | C23×#261 | semidirect |
| 158. C22 | C2×#88101 | direct (N × H) |
| 167. C2 | C22×#88101 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4⋊#261 | 2 |
| C22×#88101 | 2 |
| C23×C8×D13 | 2 |
| C23×#106 | 13 |