Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
252 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 86 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. #14545163 | C2 | semidirect |
| 2. D4×#63216 | C2 | semidirect |
| 3. #14543807 | C2 | semidirect |
| 4. #14543735 | C2 | semidirect |
| 5. D4⋊#63216 | C2 | semidirect |
| 6. #14543699 | C2 | semidirect |
| 54. #63228 | C16 | semidirect |
| 75. D4×C17 | C2×C16 | semidirect |
| 84. D68 | C2×C16 | semidirect |
| 92. #3622 | C2×C16 | semidirect |
| 158. C17 | #12062 | semidirect |
| 190. D4 | #10587529 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545163 | 2 |
| D4×#63216 | 2 |
| #14543807 | 2 |
| #14543735 | 2 |
| D4⋊#63216 | 2 |
| #14543699 | 2 |
| #14527576 | 2 |
| #12062 | 17 |