Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 141 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×#13095498 | C2 | semidirect |
| 2. C2×#15690817 | C2 | semidirect |
| 4. #20260983 | C2 | semidirect |
| 5. #20260966 | C2 | semidirect |
| 6. #20260771 | C2 | semidirect |
| 7. #20260744 | C2 | semidirect |
| 8. #20260739 | C2 | semidirect |
| 9. #536×C97 | C2 | semidirect |
| 16. C2×#13095495 | C22 | semidirect |
| 18. C22×#11715895 | C22 | semidirect |
| 24. #15690743 | C22 | semidirect |
| 25. #15690741 | C22 | semidirect |
| 26. #15690734 | C22 | semidirect |
| 33. C22⋊Q8×C97 | C22 | semidirect |
| 46. C2×#11715895 | D4 | semidirect |
| 121. C97 | #3057 | semidirect |
| 124. #536 | D97 | semidirect |
| 147. C22⋊Q8 | C2×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095498 | 2 |
| C2×#15690817 | 2 |
| #20261299 | 2 |
| #20260983 | 2 |
| #20260966 | 2 |
| #20260771 | 2 |
| #20260744 | 2 |
| #20260739 | 2 |
| #536×C97 | 2 |
| #3057 | 97 |