Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
534 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 134 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. C4×#10587529 | C2 | semidirect |
| 3. C4×#10587534 | C2 | semidirect |
| 4. #14543841 | C2 | semidirect |
| 9. #11763721 | C4 | direct (N × H) |
| 15. C4×D136 | C4 | semidirect |
| 16. D8×Dic17 | C4 | semidirect |
| 17. #11762891 | C4 | semidirect |
| 23. C4×D8×C17 | C4 | semidirect |
| 47. #10587534 | C2×C4 | semidirect |
| 49. #10587529 | C2×C4 | semidirect |
| 82. D8×C17 | C42 | semidirect |
| 100. D136 | C42 | semidirect |
| 166. C4×C17 | #357 | semidirect |
| 171. Dic17 | #357 | semidirect |
| 181. C4×D8 | #595 | semidirect |
| 235. C17 | C4×#357 | semidirect |
| 257. D8 | C4×#595 | semidirect |
| 339. C4 | #11763721 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763721 | 2 |
| C4×#10587529 | 2 |
| C4×#10587534 | 2 |
| #14543841 | 2 |
| C4×D8×D17 | 2 |
| C4×#357 | 17 |