Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
698 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 148 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. #14544699 | C2 | semidirect |
| 2. #14544498 | C2 | semidirect |
| 3. C2×D4⋊#3624 | C2 | semidirect |
| 23. C17×#127 | C8 | semidirect |
| 38. C4×#3624 | D4 | semidirect |
| 148. #127 | #3624 | semidirect |
| 164. C17 | #9642 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544699 | 2 |
| #14544498 | 2 |
| C2×D4⋊#3624 | 2 |
| #127×Dic17 | 2 |
| #9642 | 17 |