Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 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. C2×#15690830 | C2 | semidirect |
| 2. #20261406 | C2 | semidirect |
| 3. #20261111 | C2 | semidirect |
| 4. #20260969 | C2 | semidirect |
| 5. #20260935 | C2 | semidirect |
| 6. #20260932 | C2 | semidirect |
| 7. #20260880 | C2 | semidirect |
| 8. #20260878 | C2 | semidirect |
| 9. C4×#13095501 | C2 | semidirect |
| 10. D4×#11715895 | C2 | semidirect |
| 11. #550×C97 | C2 | semidirect |
| 51. #13095501 | D4 | semidirect |
| 131. C4×C97 | #135 | semidirect |
| 143. C97 | #3287 | semidirect |
| 146. #550 | D97 | semidirect |
| 276. C4 | #15690830 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690830 | 2 |
| #20261406 | 2 |
| #20261111 | 2 |
| #20260969 | 2 |
| #20260935 | 2 |
| #20260932 | 2 |
| #20260880 | 2 |
| #20260878 | 2 |
| C4×#13095501 | 2 |
| D4×#11715895 | 2 |
| #550×C97 | 2 |
| #3287 | 97 |