Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
420 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 99 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. #14529761 | C2 | semidirect |
| 3. #14528901 | C2 | semidirect |
| 4. #14527475 | C2 | semidirect |
| 6. #14526658 | C2 | semidirect |
| 98. C42×C17 | SD16 | semidirect |
| 257. C17 | #10521 | semidirect |
| 304. C42 | #63229 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14540100 | 2 |
| #14529761 | 2 |
| #14528901 | 2 |
| #14527475 | 2 |
| #14527461 | 2 |
| #14526658 | 2 |
| C17×#1962 | 2 |
| #10521 | 17 |