Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
494 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 494 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×#15690832 | C2 | semidirect |
| 2. #20261406 | C2 | semidirect |
| 3. #20261390 | C2 | semidirect |
| 4. #20261108 | C2 | semidirect |
| 5. #20260964 | C2 | semidirect |
| 6. #20260946 | C2 | semidirect |
| 7. #20260931 | C2 | semidirect |
| 8. #20260899 | C2 | semidirect |
| 9. #20260882 | C2 | semidirect |
| 10. C4×#13095500 | C2 | semidirect |
| 11. C8×D4×C97 | C2 | semidirect |
| 61. #13095500 | D4 | semidirect |
| 127. C4×C97 | #135 | semidirect |
| 141. C97 | #3284 | semidirect |
| 152. C8×D4 | D97 | semidirect |
| 272. C4 | #15690832 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690832 | 2 |
| #20261406 | 2 |
| #20261390 | 2 |
| #20261108 | 2 |
| #20260964 | 2 |
| #20260946 | 2 |
| #20260931 | 2 |
| #20260899 | 2 |
| #20260882 | 2 |
| C4×#13095500 | 2 |
| C8×D4×C97 | 2 |
| #3284 | 97 |