Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
662 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 184 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×#11763851 | C2 | semidirect |
| 2. #14545183 | C2 | direct (N × H) |
| 3. C2×#11763737 | C2 | semidirect |
| 4. C2×#11763723 | C2 | semidirect |
| 5. C2×C16×#595 | C2 | semidirect |
| 10. #11763851 | C22 | semidirect |
| 14. #11763737 | C22 | semidirect |
| 15. #11763723 | C22 | semidirect |
| 16. C16×#595 | C22 | semidirect |
| 18. #11763238 | C4 | semidirect |
| 20. C2×Dic136 | C4 | semidirect |
| 21. C2×#10587498 | C4 | semidirect |
| 23. C2×C17×D16 | C4 | semidirect |
| 48. C17×D16 | C2×C4 | semidirect |
| 50. #10587498 | C2×C4 | semidirect |
| 52. Dic136 | C2×C4 | semidirect |
| 142. C2×D16 | #595 | semidirect |
| 154. C2×C17 | #2178 | semidirect |
| 176. D16 | C2×#595 | semidirect |
| 189. C17 | C2×#2178 | semidirect |
| 267. C2 | #14545183 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763851 | 2 |
| #14545183 | 2 |
| C2×#11763737 | 2 |
| C2×#11763723 | 2 |
| C2×C16×#595 | 2 |
| C2×#11763238 | 2 |
| C2×#2178 | 17 |