Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
372 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 133 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. #20261363 | C2 | semidirect |
| 3. #20261104 | C2 | semidirect |
| 4. #20261095 | C2 | semidirect |
| 5. #20261090 | C2 | semidirect |
| 6. #20261086 | C2 | semidirect |
| 7. #20260745 | C2 | semidirect |
| 10. C2×#15690735 | C2 | semidirect |
| 11. #405×C97 | C2 | semidirect |
| 128. C97 | #3137 | semidirect |
| 139. #405 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261363 | 2 |
| #20261311 | 2 |
| #20261104 | 2 |
| #20261095 | 2 |
| #20261090 | 2 |
| #20261086 | 2 |
| #20260745 | 2 |
| #20260737 | 2 |
| #20260732 | 2 |
| C2×#15690735 | 2 |
| #405×C97 | 2 |
| #3137 | 97 |