Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
4990 conjugacy classes of subgroups; only the 1208 normal subgroups are shown.
This group has 4990 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 |
|---|---|---|
| 2. C22×#10587545 | C2 | direct (N × H) |
| 7. C2×#10587545 | C22 | direct (N × H) |
| 35. #10587545 | C23 | direct (N × H) |
| 64. C23×C17 | #101 | semidirect |
| 88. C22×C17 | C2×#101 | semidirect |
| 109. C2×C17 | C22×#101 | semidirect |
| 132. C17 | C23×#101 | semidirect |
| 160. C23 | #10587545 | direct (N × H) |
| 181. C22 | C2×#10587545 | direct (N × H) |
| 191. C2 | C22×#10587545 | 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×#10587545 | 2 |
| C24×Dic34 | 2 |
| C23×#101 | 17 |