Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
2046 conjugacy classes of subgroups; only the 1077 normal subgroups are shown.
This group has 2046 conjugacy classes of subgroups — too many to draw. Only its 1077 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. C42×#3633 | C2 | direct (N × H) |
| 5. C2×C4×#3633 | C4 | direct (N × H) |
| 17. C2×C4×#595 | C8 | semidirect |
| 22. C4×#3633 | C2×C4 | direct (N × H) |
| 23. C2×C42×C17 | C8 | semidirect |
| 24. C2×C4×Dic17 | C8 | semidirect |
| 25. C42×D17 | C8 | semidirect |
| 34. C2×#3633 | C42 | direct (N × H) |
| 43. C4×#595 | C2×C8 | semidirect |
| 45. C42×C17 | C2×C8 | semidirect |
| 46. C4×Dic17 | C2×C8 | semidirect |
| 53. C2×#595 | C4×C8 | semidirect |
| 59. #3633 | C2×C42 | direct (N × H) |
| 60. C2×C4×C17 | C4×C8 | semidirect |
| 62. C2×Dic17 | C4×C8 | semidirect |
| 64. C4×D17 | C4×C8 | semidirect |
| 78. #595 | C2×C4×C8 | semidirect |
| 80. C4×C17 | C2×C4×C8 | semidirect |
| 81. Dic17 | C2×C4×C8 | semidirect |
| 90. C2×C17 | C42×C8 | semidirect |
| 92. D17 | C42×C8 | semidirect |
| 108. C2×C42 | #3633 | direct (N × H) |
| 110. C17 | C2×C42×C8 | semidirect |
| 130. C42 | C2×#3633 | direct (N × H) |
| 147. C2×C4 | C4×#3633 | direct (N × H) |
| 161. C4 | C2×C4×#3633 | direct (N × H) |
| 165. C2 | C42×#3633 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×#3633 | 2 |
| C42×#3633 | 2 |
| C2×C42×#595 | 2 |
| C2×C42×C8 | 17 |