Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
390 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 86 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. #14544723 | C2 | semidirect |
| 3. #14544361 | C2 | semidirect |
| 5. #14543670 | C2 | semidirect |
| 6. #14543616 | C2 | semidirect |
| 111. D4×C17 | #108 | semidirect |
| 233. C17 | #8898 | semidirect |
| 281. D4 | #10587535 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545712 | 2 |
| #14544723 | 2 |
| #14544361 | 2 |
| #14544120 | 2 |
| #14543670 | 2 |
| #14543616 | 2 |
| #14527163 | 2 |
| #8898 | 17 |