Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
144 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 81 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. #20260559 | C2 | semidirect |
| 6. #15690750 | C4 | semidirect |
| 8. C2×#13095486 | C4 | semidirect |
| 56. C97 | #2155 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690750 | 2 |
| #20260773 | 2 |
| #20260559 | 2 |
| C2×#108×C97 | 2 |
| #2155 | 97 |