Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
456 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 181 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 |
|---|---|---|
| 4. #20260839 | C2 | semidirect |
| 5. #20260827 | C2 | semidirect |
| 11. C2×#13095501 | C4 | semidirect |
| 99. C97 | #2950 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095501 | 2 |
| #20261213 | 2 |
| #20261212 | 2 |
| #20260839 | 2 |
| #20260827 | 2 |
| #20260771 | 2 |
| #20260745 | 2 |
| #20260693 | 2 |
| #419×C97 | 2 |
| #2950 | 97 |