Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
300 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 3. #20260693 | C2 | semidirect |
| 4. C2×C4×#11715895 | C2 | semidirect |
| 5. #20260499 | C2 | semidirect |
| 6. #20260495 | C2 | semidirect |
| 9. #15690817 | C4 | semidirect |
| 16. #15690734 | C4 | semidirect |
| 17. #15690731 | C4 | semidirect |
| 24. #104×C97 | C4 | semidirect |
| 99. C97 | #1764 | semidirect |
| 118. #104 | Dic97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690817 | 2 |
| #20260731 | 2 |
| #20260693 | 2 |
| C2×C4×#11715895 | 2 |
| #20260499 | 2 |
| #20260495 | 2 |
| C2×#104×C97 | 2 |
| #1764 | 97 |