Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
358 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 121 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. #20261039 | C2 | semidirect |
| 4. #20260942 | C2 | semidirect |
| 6. #20260840 | C2 | semidirect |
| 7. C4×#13095501 | C2 | semidirect |
| 96. C97 | #3127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261212 | 2 |
| #20261073 | 2 |
| #20261039 | 2 |
| #20260942 | 2 |
| #20260890 | 2 |
| #20260840 | 2 |
| C4×#13095501 | 2 |
| #20260796 | 2 |
| #541×C97 | 2 |
| #3127 | 97 |