Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
470 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 131 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×#11763242 | C2 | semidirect |
| 2. C2×#11763238 | C2 | semidirect |
| 3. #14531092 | C2 | direct (N × H) |
| 4. C2×#11762649 | C2 | semidirect |
| 5. C2×#11762648 | C2 | semidirect |
| 6. C2×#11762644 | C2 | semidirect |
| 7. C2×C32×D17 | C2 | semidirect |
| 8. C2×C17×SD64 | C2 | semidirect |
| 12. #11763242 | C22 | semidirect |
| 14. #11763238 | C22 | semidirect |
| 20. #11762649 | C22 | semidirect |
| 21. #11762648 | C22 | semidirect |
| 22. #11762644 | C22 | semidirect |
| 24. C32×D17 | C22 | semidirect |
| 27. C17×SD64 | C22 | semidirect |
| 118. C2×SD64 | D17 | semidirect |
| 148. SD64 | C2×D17 | semidirect |
| 154. C2×C17 | #2262 | semidirect |
| 187. C17 | C2×#2262 | semidirect |
| 257. C2 | #14531092 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763242 | 2 |
| C2×#11763238 | 2 |
| #14531092 | 2 |
| C2×#11762649 | 2 |
| C2×#11762648 | 2 |
| C2×#11762644 | 2 |
| C2×C32×D17 | 2 |
| C2×C17×SD64 | 2 |
| C2×#2262 | 17 |