Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
12446 conjugacy classes of subgroups; only the 6264 normal subgroups are shown.
This group has 12446 conjugacy classes of subgroups — too many to draw. Only its 6264 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×Q8×#261 | C2 | direct (N × H) |
| 7. C23×Q8×C13 | C4 | semidirect |
| 8. C22×Q8×D13 | C4 | semidirect |
| 11. C23×Dic26 | C4 | semidirect |
| 12. C2×Q8×#261 | C22 | direct (N × H) |
| 17. C23×#261 | Q8 | direct (N × H) |
| 20. C22×Q8×C13 | C2×C4 | semidirect |
| 23. C2×Q8×D13 | C2×C4 | semidirect |
| 27. C22×Dic26 | C2×C4 | semidirect |
| 28. Q8×#261 | C23 | direct (N × H) |
| 38. C22×#261 | C2×Q8 | direct (N × H) |
| 41. C2×Q8×C13 | C22×C4 | semidirect |
| 44. Q8×D13 | C22×C4 | semidirect |
| 48. C2×Dic26 | C22×C4 | semidirect |
| 55. C23×C13 | C4×Q8 | semidirect |
| 57. C22×D13 | C4×Q8 | semidirect |
| 63. C2×#261 | C22×Q8 | direct (N × H) |
| 66. Q8×C13 | C23×C4 | semidirect |
| 71. Dic26 | C23×C4 | semidirect |
| 75. C23×Q8 | #261 | direct (N × H) |
| 82. C22×C13 | C2×C4×Q8 | semidirect |
| 84. C2×D13 | C2×C4×Q8 | semidirect |
| 90. #261 | C23×Q8 | direct (N × H) |
| 97. C22×Q8 | C2×#261 | direct (N × H) |
| 109. C2×C13 | C22×C4×Q8 | semidirect |
| 111. D13 | C22×C4×Q8 | semidirect |
| 122. C2×Q8 | C22×#261 | direct (N × H) |
| 133. C13 | C23×C4×Q8 | semidirect |
| 139. C23 | Q8×#261 | direct (N × H) |
| 142. Q8 | C23×#261 | direct (N × H) |
| 156. C22 | C2×Q8×#261 | direct (N × H) |
| 165. C2 | C22×Q8×#261 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×#261 | 2 |
| C23×C4⋊#261 | 2 |
| C23×C4×#261 | 2 |
| C23×Q8×D13 | 2 |
| C23×C4×Q8 | 13 |