Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
578 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 3. #14545785 | C2 | semidirect |
| 4. #14545784 | C2 | semidirect |
| 47. C17×C22⋊Q8 | C8 | semidirect |
| 48. #10587632 | C8 | semidirect |
| 49. #10587610 | C8 | semidirect |
| 50. #10587583 | C8 | semidirect |
| 83. C2×Q8×C17 | C2×C8 | semidirect |
| 97. C2×Dic34 | C2×C8 | semidirect |
| 111. C4⋊C4×C17 | C2×C8 | semidirect |
| 117. C4⋊Dic17 | C2×C8 | semidirect |
| 258. C22⋊Q8 | #3633 | semidirect |
| 282. C17 | #7589 | semidirect |
| 288. C2×Q8 | C2×#3633 | semidirect |
| 331. C4⋊C4 | C2×#3633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545924 | 2 |
| C2×(C2×#3633)⋊C4 | 2 |
| #14545785 | 2 |
| #14545784 | 2 |
| C22⋊Q8×#595 | 2 |
| #7589 | 17 |