Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
640 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 640 conjugacy classes of subgroups — too many to draw. Only its 100 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. #14544510 | C2 | semidirect |
| 2. #14544447 | C2 | semidirect |
| 3. #14543602 | C2 | semidirect |
| 4. #14543600 | C2 | semidirect |
| 66. C2×D4×C17 | M16 | semidirect |
| 98. C4⋊C4×C17 | M16 | semidirect |
| 267. C17 | #7633 | semidirect |
| 276. C2×D4 | #63247 | semidirect |
| 311. C4⋊C4 | #63247 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544510 | 2 |
| #14544447 | 2 |
| #14543602 | 2 |
| #14543600 | 2 |
| #121×Dic17 | 2 |
| #7633 | 17 |