Order 4352.
5206 conjugacy classes of subgroups.
The subgroup lattice has 388 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#10587680 | C2 | semidirect |
| 2. #14545373 | C2 | direct (N × H) |
| 3. C2×#11763784 | C2 | semidirect |
| 4. C2×#11763780 | C2 | semidirect |
| 5. C2×#11763777 | C2 | semidirect |
| 8. C2×#10587680 | C22 | semidirect |
| 9. C22×#63243 | C22 | semidirect |
| 10. C22×#63242 | C22 | semidirect |
| 11. #11763784 | C22 | semidirect |
| 12. #11763780 | C22 | semidirect |
| 13. C2×#10587543 | C22 | semidirect |
| 14. C2×#10587543 | C22 | semidirect |
| 15. #11763777 | C22 | semidirect |
| 63. C2×#63243 | C23 | semidirect |
| 65. C2×#63242 | C23 | semidirect |
| 68. #10587543 | C23 | semidirect |
| 69. #10587543 | C23 | semidirect |
| 125. C23×C17 | #131 | semidirect |
| 176. C22×C17 | C2×#131 | semidirect |
| 215. C2×C17 | #2880 | semidirect |
| 263. C17 | C2×#2880 | semidirect |
| 330. C23 | #10587680 | semidirect |
| 372. C22 | C2×#10587680 | semidirect |
| 383. C2 | #14545373 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10587680 | 2 |
| #14545373 | 2 |
| C2×#11763784 | 2 |
| C2×#11763780 | 2 |
| C2×#11763777 | 2 |
| C23×#63256 | 2 |
| C2×#2880 | 17 |