Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
250 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 147 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. #14526918 | C2 | semidirect |
| 4. C32×Dic17 | C2 | semidirect |
| 5. C17×#1397 | C2 | semidirect |
| 9. #11762642 | C4 | semidirect |
| 29. C17×C32 | C2×C4 | semidirect |
| 30. #10587465 | C2×C4 | semidirect |
| 64. #1397 | D17 | semidirect |
| 73. Dic17 | M64 | semidirect |
| 101. C32 | C4×D17 | semidirect |
| 102. C17 | C4×M64 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11762642 | 2 |
| C4×C16×D17 | 2 |
| #14526918 | 2 |
| C32×Dic17 | 2 |
| C17×#1397 | 2 |
| C4×M64 | 17 |