Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
516 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 125 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. C42×#3622 | C2 | semidirect |
| 4. #14527539 | C2 | semidirect |
| 5. #14527238 | C2 | semidirect |
| 9. #11763205 | C4 | semidirect |
| 10. #11763181 | C4 | semidirect |
| 11. #11763161 | C4 | semidirect |
| 12. #11763155 | C4 | semidirect |
| 89. C42×C17 | SD16 | semidirect |
| 142. #3622 | #104 | semidirect |
| 231. C17 | #9843 | semidirect |
| 271. C42 | #63229 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539339 | 2 |
| #14529761 | 2 |
| C42×#3622 | 2 |
| #14527539 | 2 |
| #14527238 | 2 |
| #14527235 | 2 |
| C17×#1962 | 2 |
| #9843 | 17 |