Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
214 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 103 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. C22×#10587528 | C2 | semidirect |
| 2. C4⋊#10587528 | C2 | semidirect |
| 3. C22⋊#10587528 | C2 | semidirect |
| 4. C4×#10587528 | C2 | semidirect |
| 24. #10587528 | D4 | direct (N × H) |
| 44. D4×C17 | C32 | semidirect |
| 62. C22×C17 | C2×C32 | semidirect |
| 66. C4×C17 | C2×C32 | semidirect |
| 95. C17 | D4×C32 | semidirect |
| 111. D4 | #10587528 | direct (N × H) |
| 124. C22 | C2×#10587528 | semidirect |
| 128. C4 | C2×#10587528 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10587528 | 2 |
| C4⋊#10587528 | 2 |
| C22⋊#10587528 | 2 |
| C4×#10587528 | 2 |
| D4×#63216 | 2 |
| D4×C32 | 17 |