Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
454 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 168 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 |
|---|---|---|
| 12. C8×#3622 | C4 | semidirect |
| 13. C8×#3622 | C4 | semidirect |
| 14. C8×#3622 | C4 | semidirect |
| 15. C82×C17 | C4 | semidirect |
| 71. C8×C17 | #106 | semidirect |
| 72. C8×C17 | #107 | semidirect |
| 74. #3622 | #106 | semidirect |
| 75. #3622 | #107 | semidirect |
| 102. C82 | #595 | semidirect |
| 126. C17 | #8814 | semidirect |
| 166. C8 | #10587533 | semidirect |
| 167. C8 | #10587534 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544720 | 2 |
| #14544719 | 2 |
| #14544705 | 2 |
| C82×D17 | 2 |
| #8814 | 17 |