Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
184 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 93 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. #20261830 | C2 | semidirect |
| 4. #20261828 | C2 | semidirect |
| 6. #15690907 | C4 | semidirect |
| 7. #15690906 | C4 | semidirect |
| 8. #15690905 | C4 | semidirect |
| 12. C2×#13095523 | C4 | semidirect |
| 63. C97 | #2108 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261854 | 2 |
| C2×#15690905 | 2 |
| #20261830 | 2 |
| #20261828 | 2 |
| #20261701 | 2 |
| #2108 | 97 |