Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
774 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 774 conjugacy classes of subgroups — too many to draw. Only its 192 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. #14544716 | C2 | semidirect |
| 2. C42×#3624 | C2 | semidirect |
| 3. C2×D4⋊#3624 | C2 | semidirect |
| 23. C17×#127 | C8 | semidirect |
| 41. C4×#3624 | D4 | semidirect |
| 123. C4×C17 | D4⋊C8 | semidirect |
| 156. #127 | #3624 | semidirect |
| 175. C17 | #9638 | semidirect |
| 258. C4 | D4⋊#3624 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544716 | 2 |
| C42×#3624 | 2 |
| C2×D4⋊#3624 | 2 |
| #127×Dic17 | 2 |
| #9638 | 17 |