Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
264 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 264 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 |
|---|---|---|
| 1. #20260792 | C2 | semidirect |
| 2. C4×#13095495 | C2 | semidirect |
| 3. #20260475 | C2 | semidirect |
| 8. #15690721 | C22 | semidirect |
| 9. #15690721 | C22 | semidirect |
| 85. C97 | #1527 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20260792 | 2 |
| C4×#13095495 | 2 |
| #20260475 | 2 |
| C2×#124×C97 | 2 |
| #1527 | 97 |