Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
654 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 654 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×#11763853 | C2 | semidirect |
| 2. #14545187 | C2 | direct (N × H) |
| 3. C2×#11763738 | C2 | semidirect |
| 4. C2×#11763724 | C2 | semidirect |
| 5. C2×#11763696 | C2 | semidirect |
| 10. #11763853 | C22 | semidirect |
| 14. #11763738 | C22 | semidirect |
| 15. #11763724 | C22 | semidirect |
| 16. #11763696 | C22 | semidirect |
| 18. #11763242 | C4 | semidirect |
| 20. C2×#10587499 | C4 | semidirect |
| 21. C2×D272 | C4 | semidirect |
| 23. C2×C17×Q32 | C4 | semidirect |
| 48. C17×Q32 | C2×C4 | semidirect |
| 50. #10587499 | C2×C4 | semidirect |
| 52. D272 | C2×C4 | semidirect |
| 138. C2×Q32 | #595 | semidirect |
| 151. C2×C17 | #2179 | semidirect |
| 172. Q32 | C2×#595 | semidirect |
| 187. C17 | C2×#2179 | semidirect |
| 263. C2 | #14545187 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763853 | 2 |
| #14545187 | 2 |
| C2×#11763738 | 2 |
| C2×#11763724 | 2 |
| C2×#11763696 | 2 |
| C2×#11763242 | 2 |
| C2×#2179 | 17 |