Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
492 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×#13095500 | C2 | semidirect |
| 2. #20261306 | C2 | semidirect |
| 4. #20260981 | C2 | semidirect |
| 5. #20260964 | C2 | semidirect |
| 6. #20260773 | C2 | semidirect |
| 7. #20260745 | C2 | semidirect |
| 8. #20260741 | C2 | semidirect |
| 9. C2×#131×C97 | C2 | semidirect |
| 20. #15690789 | C22 | semidirect |
| 25. #15690744 | C22 | semidirect |
| 26. #15690742 | C22 | semidirect |
| 27. #15690735 | C22 | semidirect |
| 32. C2×M16×C97 | C22 | semidirect |
| 34. C22×C8×C97 | C22 | semidirect |
| 67. C2×C8×C97 | D4 | semidirect |
| 121. C97 | #3057 | semidirect |
| 123. C2×#131 | D97 | semidirect |
| 139. C2×M16 | C2×D97 | semidirect |
| 141. C22×C8 | C2×D97 | semidirect |
| 179. C2×C8 | C22⋊D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095500 | 2 |
| #20261306 | 2 |
| #20261299 | 2 |
| #20260981 | 2 |
| #20260964 | 2 |
| #20260773 | 2 |
| #20260745 | 2 |
| #20260741 | 2 |
| C2×#131×C97 | 2 |
| #3057 | 97 |