Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
12446 conjugacy classes of subgroups; only the 8971 normal subgroups are shown.
This group has 12446 conjugacy classes of subgroups — too many to draw. Only its 8971 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×Dic17 | C2 | direct (N × H) |
| 7. C2×Q8×Dic17 | C22 | direct (N × H) |
| 10. C23×Q8×C17 | C4 | semidirect |
| 14. C22×Q8×C17 | C2×C4 | semidirect |
| 19. C23×Dic17 | Q8 | direct (N × H) |
| 22. Q8×Dic17 | C23 | direct (N × H) |
| 29. C2×Q8×C17 | C22×C4 | semidirect |
| 34. C22×Dic17 | C2×Q8 | direct (N × H) |
| 40. C23×C17 | C4×Q8 | semidirect |
| 45. Q8×C17 | C23×C4 | semidirect |
| 49. C2×Dic17 | C22×Q8 | direct (N × H) |
| 56. C22×C17 | C2×C4×Q8 | semidirect |
| 63. Dic17 | C23×Q8 | direct (N × H) |
| 64. C23×Q8 | Dic17 | direct (N × H) |
| 72. C2×C17 | C22×C4×Q8 | semidirect |
| 77. C22×Q8 | C2×Dic17 | direct (N × H) |
| 88. C17 | C23×C4×Q8 | semidirect |
| 93. C2×Q8 | C22×Dic17 | direct (N × H) |
| 103. C23 | Q8×Dic17 | direct (N × H) |
| 108. Q8 | C23×Dic17 | direct (N × H) |
| 115. C22 | C2×Q8×Dic17 | direct (N × H) |
| 123. C2 | C22×Q8×Dic17 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×Dic17 | 2 |
| C23×C4⋊Dic17 | 2 |
| C23×C4×Dic17 | 2 |
| C24×Q8×C17 | 2 |
| C23×C4×Q8 | 17 |