Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
512 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 269 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. #20260771 | C2 | direct (N × H) |
| 4. C2×#15690743 | C2 | semidirect |
| 5. C2×#15690741 | C2 | semidirect |
| 7. C22×#11715895 | C4 | semidirect |
| 16. #15690743 | C22 | semidirect |
| 17. #15690741 | C22 | semidirect |
| 27. C2×#11715895 | C2×C4 | semidirect |
| 78. C2×C97 | #427 | semidirect |
| 82. C97 | C2×#427 | semidirect |
| 160. C2 | #20260771 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11715895 | 2 |
| C2×#15690769 | 2 |
| #20260771 | 2 |
| C2×#15690743 | 2 |
| C2×#15690741 | 2 |
| C2×#117×C97 | 2 |
| C2×#427 | 97 |