Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
492 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 189 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 |
|---|---|---|
| 3. #20260833 | C2 | semidirect |
| 4. C4×#13095498 | C2 | semidirect |
| 5. #20260771 | C2 | semidirect |
| 6. #20260744 | C2 | semidirect |
| 8. #20260691 | C2 | semidirect |
| 9. #519×C97 | C2 | semidirect |
| 11. C2×#13095498 | C4 | semidirect |
| 20. #15690743 | C22 | semidirect |
| 21. #15690741 | C22 | semidirect |
| 22. #15690734 | C22 | semidirect |
| 24. #15690721 | C22 | semidirect |
| 25. C4×#11715895 | C22 | semidirect |
| 28. C4×Q8×C97 | C22 | semidirect |
| 38. #13095498 | C2×C4 | semidirect |
| 39. #13095498 | C2×C4 | semidirect |
| 41. C2×#11715895 | C2×C4 | semidirect |
| 51. C2×Q8×C97 | C2×C4 | semidirect |
| 104. C97 | #2949 | semidirect |
| 106. #519 | D97 | semidirect |
| 122. C4×Q8 | C2×D97 | semidirect |
| 139. C2×Q8 | C4×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095498 | 2 |
| #20261209 | 2 |
| #20260833 | 2 |
| C4×#13095498 | 2 |
| #20260771 | 2 |
| #20260744 | 2 |
| #20260739 | 2 |
| #20260691 | 2 |
| #519×C97 | 2 |
| #2949 | 97 |