Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
232 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 57 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. #14530630 | C2 | semidirect |
| 5. #14526979 | C2 | semidirect |
| 6. #14526961 | C2 | semidirect |
| 7. C17×#1415 | C2 | semidirect |
| 38. D272 | D4 | semidirect |
| 88. #1415 | D17 | semidirect |
| 103. Dic17 | D32 | semidirect |
| 143. C17 | #13685 | 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 |
| #14530630 | 2 |
| #14526979 | 2 |
| #14526961 | 2 |
| C17×#1415 | 2 |
| #13685 | 17 |