Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
270 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 67 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. C2×D544 | C2 | semidirect |
| 2. C2×#11762644 | C2 | semidirect |
| 3. #14531032 | C2 | semidirect |
| 4. C32×Dic17 | C2 | semidirect |
| 5. C2×C17×D32 | C2 | semidirect |
| 28. C17×C32 | D4 | semidirect |
| 29. #10587465 | D4 | semidirect |
| 59. C2×D32 | D17 | semidirect |
| 69. Dic17 | D32 | semidirect |
| 97. C32 | C22⋊D17 | semidirect |
| 98. C17 | #13725 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D544 | 2 |
| C2×#11762644 | 2 |
| #14531032 | 2 |
| C32×Dic17 | 2 |
| C2×C17×D32 | 2 |
| #13725 | 17 |