Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
386 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 123 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. #20261455 | C2 | semidirect |
| 3. #20261086 | C2 | semidirect |
| 4. #20261077 | C2 | semidirect |
| 5. #20261016 | C2 | semidirect |
| 6. #20260976 | C2 | semidirect |
| 7. #20260946 | C2 | semidirect |
| 8. #20260899 | C2 | semidirect |
| 9. C4×#13095500 | C2 | semidirect |
| 10. #20260732 | C2 | semidirect |
| 11. C8×D4×C97 | C2 | semidirect |
| 126. C97 | #3302 | semidirect |
| 136. C8×D4 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261455 | 2 |
| #20261390 | 2 |
| #20261086 | 2 |
| #20261077 | 2 |
| #20261016 | 2 |
| #20260976 | 2 |
| #20260946 | 2 |
| #20260899 | 2 |
| C4×#13095500 | 2 |
| #20260732 | 2 |
| C8×D4×C97 | 2 |
| #3302 | 97 |