Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
7134 conjugacy classes of subgroups; only the 1208 normal subgroups are shown.
This group has 7134 conjugacy classes of subgroups — too many to draw. Only its 1208 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. C23×#63247 | C2 | semidirect |
| 2. C22×#10587553 | C2 | direct (N × H) |
| 5. C22×#63247 | C22 | semidirect |
| 7. C2×#10587553 | C22 | direct (N × H) |
| 35. C2×#63247 | C23 | semidirect |
| 37. #10587553 | C23 | direct (N × H) |
| 67. #63247 | C24 | semidirect |
| 77. C23×C17 | #100 | semidirect |
| 106. C22×C17 | C2×#100 | semidirect |
| 130. C2×C17 | C22×#100 | semidirect |
| 156. C17 | C23×#100 | semidirect |
| 201. C23 | #10587553 | direct (N × H) |
| 225. C22 | C2×#10587553 | direct (N × H) |
| 235. C2 | C22×#10587553 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#63247 | 2 |
| C22×#10587553 | 2 |
| C24×C22⋊D17 | 2 |
| C23×#100 | 17 |