Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
440 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 98 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. #14544717 | C2 | semidirect |
| 3. #14544337 | C2 | semidirect |
| 5. #14543630 | C2 | semidirect |
| 6. #14543612 | C2 | semidirect |
| 110. C4×Dic17 | M16 | semidirect |
| 116. #63223 | M16 | semidirect |
| 256. C17 | #8841 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545705 | 2 |
| #14544717 | 2 |
| #14544337 | 2 |
| #14544081 | 2 |
| #14543630 | 2 |
| #14543612 | 2 |
| #14528588 | 2 |
| #8841 | 17 |