Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
5502 conjugacy classes of subgroups; only the 2056 normal subgroups are shown.
This group has 5502 conjugacy classes of subgroups — too many to draw. Only its 2056 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. C2×#11763755 | C2 | direct (N × H) |
| 7. #11763755 | C22 | direct (N × H) |
| 9. C22×C4×Dic17 | C4 | semidirect |
| 10. C2×C42×D17 | C4 | semidirect |
| 12. C22×C42×C17 | C4 | semidirect |
| 24. C2×C42×C17 | C2×C4 | semidirect |
| 25. C2×C4×Dic17 | C2×C4 | semidirect |
| 26. C42×D17 | C2×C4 | semidirect |
| 36. C22×C4×C17 | C4⋊C4 | semidirect |
| 38. C22×Dic17 | C4⋊C4 | semidirect |
| 40. C2×C4×D17 | C4⋊C4 | semidirect |
| 46. C42×C17 | C22×C4 | semidirect |
| 47. C4×Dic17 | C22×C4 | semidirect |
| 60. C2×C4×C17 | C2×C4⋊C4 | semidirect |
| 62. C2×Dic17 | C2×C4⋊C4 | semidirect |
| 64. C4×D17 | C2×C4⋊C4 | semidirect |
| 70. C22×C17 | #384 | semidirect |
| 73. C2×D17 | #384 | semidirect |
| 80. C4×C17 | C22×C4⋊C4 | semidirect |
| 81. Dic17 | C22×C4⋊C4 | semidirect |
| 89. C22×C42 | #595 | semidirect |
| 91. C2×C17 | C2×#384 | semidirect |
| 93. D17 | C2×#384 | semidirect |
| 110. C2×C42 | C2×#595 | semidirect |
| 111. C17 | C22×#384 | semidirect |
| 127. C22×C4 | C4⋊#595 | semidirect |
| 131. C42 | C22×#595 | semidirect |
| 148. C2×C4 | C2×C4⋊#595 | semidirect |
| 156. C22 | #11763755 | direct (N × H) |
| 161. C4 | C22×C4⋊#595 | semidirect |
| 165. C2 | C2×#11763755 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4⋊#595 | 2 |
| C2×#11763755 | 2 |
| C22×C42×D17 | 2 |
| C22×#384 | 17 |