Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
214 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 56 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. D16×#595 | C2 | semidirect |
| 2. #14543945 | C2 | semidirect |
| 3. #14543933 | C2 | semidirect |
| 4. C32×#595 | C2 | semidirect |
| 12. D544 | C4 | semidirect |
| 13. #11762644 | C4 | semidirect |
| 15. C17×D32 | C4 | semidirect |
| 22. C17×D16 | C2×C4 | semidirect |
| 24. D272 | C2×C4 | semidirect |
| 27. C17×C32 | C2×C4 | semidirect |
| 28. #10587465 | C2×C4 | semidirect |
| 67. #595 | D32 | direct (N × H) |
| 74. D32 | #595 | direct (N × H) |
| 89. D16 | C2×#595 | semidirect |
| 97. C32 | C2×#595 | semidirect |
| 98. C17 | C4×D32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D16×#595 | 2 |
| #14543945 | 2 |
| #14543933 | 2 |
| C32×#595 | 2 |
| D17×D32 | 2 |
| C4×D32 | 17 |