Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
354 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 354 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. #20261442 | C2 | semidirect |
| 3. #20261140 | C2 | semidirect |
| 4. #20261077 | C2 | semidirect |
| 5. #20261049 | C2 | semidirect |
| 6. #20261031 | C2 | semidirect |
| 7. #20261026 | C2 | semidirect |
| 8. #20260981 | C2 | semidirect |
| 9. C4×#13095500 | C2 | semidirect |
| 10. #20260777 | C2 | semidirect |
| 11. #436×C97 | C2 | semidirect |
| 122. C97 | #3357 | semidirect |
| 132. #436 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261450 | 2 |
| #20261442 | 2 |
| #20261140 | 2 |
| #20261077 | 2 |
| #20261049 | 2 |
| #20261031 | 2 |
| #20261026 | 2 |
| #20260981 | 2 |
| C4×#13095500 | 2 |
| #20260777 | 2 |
| #436×C97 | 2 |
| #3357 | 97 |