Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
614 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 614 conjugacy classes of subgroups — too many to draw. Only its 140 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. C8×C22⋊#595 | C2 | semidirect |
| 4. #14543626 | C2 | semidirect |
| 12. #11763655 | C4 | semidirect |
| 13. #11763652 | C4 | semidirect |
| 18. C2×#10587485 | C4 | semidirect |
| 19. C2×C22⋊#3622 | C4 | semidirect |
| 21. C2×C8×Dic17 | C4 | semidirect |
| 22. C23×C8×C17 | C4 | semidirect |
| 46. #10587551 | C8 | direct (N × H) |
| 75. C22⋊#595 | C2×C8 | semidirect |
| 104. C23×C17 | C4×C8 | semidirect |
| 129. C2×Dic17 | C4×C8 | semidirect |
| 137. C8×C17 | #99 | semidirect |
| 169. C23×C8 | #595 | semidirect |
| 224. C17 | C8×#99 | semidirect |
| 278. C23 | C8×#595 | semidirect |
| 308. C8 | #10587551 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#10587551 | 2 |
| C8×C22⋊#595 | 2 |
| #14544019 | 2 |
| #14543626 | 2 |
| C2×C8×C22⋊D17 | 2 |
| C8×#99 | 17 |