Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
494 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 125 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×#15690833 | C2 | semidirect |
| 2. #20261407 | C2 | semidirect |
| 3. #20261388 | C2 | semidirect |
| 4. #20261109 | C2 | semidirect |
| 5. #20260967 | C2 | semidirect |
| 6. #20260931 | C2 | semidirect |
| 7. #20260896 | C2 | semidirect |
| 8. #20260883 | C2 | semidirect |
| 9. C4×#13095498 | C2 | semidirect |
| 10. #20260800 | C2 | semidirect |
| 11. #462×C97 | C2 | semidirect |
| 60. #13095498 | D4 | semidirect |
| 129. C4×C97 | #135 | semidirect |
| 141. C97 | #3284 | semidirect |
| 147. #462 | D97 | semidirect |
| 272. C4 | #15690833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690833 | 2 |
| #20261407 | 2 |
| #20261388 | 2 |
| #20261109 | 2 |
| #20260967 | 2 |
| #20260931 | 2 |
| #20260896 | 2 |
| #20260883 | 2 |
| C4×#13095498 | 2 |
| #20260800 | 2 |
| #462×C97 | 2 |
| #3284 | 97 |