Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
550 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 550 conjugacy classes of subgroups — too many to draw. Only its 106 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 |
|---|---|---|
| 1. #14544660 | C2 | semidirect |
| 3. #14543647 | C2 | semidirect |
| 10. C23×#3622 | C4 | semidirect |
| 15. C2×#10587485 | C4 | semidirect |
| 17. C2×C8×Dic17 | C4 | semidirect |
| 18. C2×C17×C22⋊C8 | C4 | semidirect |
| 94. C23×C17 | #106 | semidirect |
| 119. C2×Dic17 | #106 | semidirect |
| 128. #3622 | #99 | semidirect |
| 165. C2×C22⋊C8 | #595 | semidirect |
| 206. C17 | #8608 | semidirect |
| 257. C23 | #10587533 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544660 | 2 |
| #14544644 | 2 |
| #14543647 | 2 |
| C2×#11762872 | 2 |
| #8608 | 17 |