Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
416 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
|---|---|---|
| 2. #14545132 | C2 | semidirect |
| 4. #14544903 | C2 | semidirect |
| 5. #14543864 | C2 | semidirect |
| 6. #14543836 | C2 | semidirect |
| 25. #11762623 | C4 | semidirect |
| 26. #11762622 | C4 | semidirect |
| 27. #11762621 | C4 | semidirect |
| 28. C17×#361 | C4 | semidirect |
| 62. C17×M32 | C2×C4 | semidirect |
| 63. C17×#108 | C2×C4 | semidirect |
| 65. #10587490 | C2×C4 | semidirect |
| 66. #10587483 | C2×C4 | semidirect |
| 191. #361 | #595 | semidirect |
| 222. M32 | C2×#595 | semidirect |
| 231. #108 | C2×#595 | semidirect |
| 239. C17 | #12953 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545543 | 2 |
| #14545132 | 2 |
| C2×#11763727 | 2 |
| #14544903 | 2 |
| #14543864 | 2 |
| #14543836 | 2 |
| D17×#361 | 2 |
| #12953 | 17 |