Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
428 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 3. C2×#11763699 | C2 | semidirect |
| 4. #14544593 | C2 | semidirect |
| 5. #14543864 | C2 | semidirect |
| 6. #14543852 | C2 | semidirect |
| 10. #11763850 | C4 | semidirect |
| 11. #11763849 | C4 | semidirect |
| 18. #11763726 | C4 | semidirect |
| 19. #11763725 | C4 | semidirect |
| 25. #11762617 | C4 | semidirect |
| 26. #11762616 | C4 | semidirect |
| 27. #11762615 | C4 | semidirect |
| 28. C17×#359 | C4 | semidirect |
| 56. #10587533 | C2×C4 | semidirect |
| 62. #10587530 | C2×C4 | semidirect |
| 63. C2×C16×C17 | C2×C4 | semidirect |
| 64. C17×#108 | C2×C4 | semidirect |
| 66. #10587490 | C2×C4 | semidirect |
| 67. C2×#63214 | C2×C4 | semidirect |
| 197. #359 | #595 | semidirect |
| 233. C2×C16 | C2×#595 | semidirect |
| 236. #108 | C2×#595 | semidirect |
| 247. C17 | #12649 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545538 | 2 |
| #14545104 | 2 |
| C2×#11763699 | 2 |
| #14544593 | 2 |
| #14543864 | 2 |
| #14543852 | 2 |
| #14530510 | 2 |
| #12649 | 17 |