Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
252 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 102 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. D4×#63216 | C2 | semidirect |
| 2. #14543806 | C2 | semidirect |
| 3. D4⋊#63216 | C2 | semidirect |
| 4. #14543697 | C2 | semidirect |
| 32. D8×C17 | C16 | semidirect |
| 50. D4×C17 | C2×C16 | semidirect |
| 58. C8×C17 | C2×C16 | semidirect |
| 106. C17 | #12062 | semidirect |
| 109. D8 | #63216 | semidirect |
| 126. D4 | C2×#63216 | semidirect |
| 138. C8 | C2×#63216 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×#63216 | 2 |
| #14543806 | 2 |
| D4⋊#63216 | 2 |
| #14543697 | 2 |
| D8×#3622 | 2 |
| #12062 | 17 |