Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
7646 conjugacy classes of subgroups; only the 1976 normal subgroups are shown.
This group has 7646 conjugacy classes of subgroups — too many to draw. Only its 1976 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. C24×#3624 | C2 | semidirect |
| 2. C22×#10587543 | C2 | direct (N × H) |
| 5. C23×#3624 | C22 | semidirect |
| 6. C2×#10587543 | C22 | direct (N × H) |
| 16. C24×D17 | C8 | semidirect |
| 28. C22×#3624 | C23 | semidirect |
| 29. #10587543 | C23 | direct (N × H) |
| 37. C23×D17 | C2×C8 | semidirect |
| 50. C2×#3624 | C24 | semidirect |
| 52. C23×C17 | C22⋊C8 | semidirect |
| 60. C22×D17 | C22×C8 | semidirect |
| 74. C22×C17 | C2×C22⋊C8 | semidirect |
| 82. C2×D17 | C23×C8 | semidirect |
| 95. C2×C17 | C22×C22⋊C8 | semidirect |
| 117. C17 | C23×C22⋊C8 | semidirect |
| 144. C23 | #10587543 | direct (N × H) |
| 162. C22 | C2×#10587543 | direct (N × H) |
| 171. C2 | C22×#10587543 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×#3624 | 2 |
| C22×#10587543 | 2 |
| C24×C4×D17 | 2 |
| C23×C22⋊C8 | 17 |