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. #14544999 | C2 | semidirect |
| 4. #14544592 | C2 | semidirect |
| 5. #14543865 | C2 | semidirect |
| 6. #14543851 | C2 | semidirect |
| 10. #11763850 | C4 | semidirect |
| 11. #11763850 | C4 | semidirect |
| 12. #11763849 | C4 | semidirect |
| 13. #11763849 | C4 | semidirect |
| 21. #11763724 | C4 | semidirect |
| 22. #11763723 | C4 | semidirect |
| 29. #11762620 | C4 | semidirect |
| 30. #11762619 | C4 | semidirect |
| 31. #11762618 | C4 | semidirect |
| 32. C17×#360 | C4 | semidirect |
| 65. #10587536 | C2×C4 | semidirect |
| 74. #10587529 | C2×C4 | semidirect |
| 75. C17×M32 | C2×C4 | semidirect |
| 76. C17×#106 | C2×C4 | semidirect |
| 77. #10587488 | C2×C4 | semidirect |
| 78. #10587483 | C2×C4 | semidirect |
| 225. #360 | #595 | semidirect |
| 265. M32 | C2×#595 | semidirect |
| 275. #106 | C2×#595 | semidirect |
| 286. C17 | #12649 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545538 | 2 |
| #14545098 | 2 |
| #14544999 | 2 |
| #14544592 | 2 |
| #14543865 | 2 |
| #14543851 | 2 |
| #14530518 | 2 |
| #12649 | 17 |