Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
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×#10587533 | C2 | direct (N × H) |
| 7. C2×#10587533 | C22 | direct (N × H) |
| 9. C23×#3622 | C4 | semidirect |
| 10. C22×C8×D17 | C4 | semidirect |
| 12. C23×C8×C17 | C4 | semidirect |
| 24. C22×C8×C17 | C2×C4 | semidirect |
| 25. C22×#3622 | C2×C4 | semidirect |
| 26. C2×C8×D17 | C2×C4 | semidirect |
| 28. #10587533 | C23 | direct (N × H) |
| 46. C2×C8×C17 | C22×C4 | semidirect |
| 47. C2×#3622 | C22×C4 | semidirect |
| 48. C8×D17 | C22×C4 | semidirect |
| 51. C23×C17 | #106 | semidirect |
| 53. C22×D17 | #106 | semidirect |
| 68. C8×C17 | C23×C4 | semidirect |
| 69. #3622 | C23×C4 | semidirect |
| 73. C22×C17 | C2×#106 | semidirect |
| 75. C2×D17 | C2×#106 | semidirect |
| 89. C23×C8 | #595 | semidirect |
| 93. C2×C17 | C22×#106 | semidirect |
| 95. D17 | C22×#106 | semidirect |
| 109. C22×C8 | C2×#595 | semidirect |
| 113. C17 | C23×#106 | semidirect |
| 132. C2×C8 | C22×#595 | semidirect |
| 139. C23 | #10587533 | direct (N × H) |
| 153. C8 | C23×#595 | semidirect |
| 158. C22 | C2×#10587533 | direct (N × H) |
| 167. C2 | C22×#10587533 | 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 |
| C22×#10587533 | 2 |
| C23×C8×D17 | 2 |
| C23×#106 | 17 |