Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 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×#13095499 | C2 | semidirect |
| 2. #20261306 | C2 | semidirect |
| 3. #20261210 | C2 | semidirect |
| 4. #20260948 | C2 | semidirect |
| 5. #20260938 | C2 | semidirect |
| 6. #20260763 | C2 | semidirect |
| 7. #20260745 | C2 | semidirect |
| 8. #20260731 | C2 | semidirect |
| 14. #15690808 | C22 | semidirect |
| 15. #15690797 | C22 | semidirect |
| 23. #15690739 | C22 | semidirect |
| 24. #15690735 | C22 | semidirect |
| 25. #15690734 | C22 | semidirect |
| 26. #15690731 | C22 | semidirect |
| 117. C97 | #3042 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095499 | 2 |
| #20261306 | 2 |
| #20261210 | 2 |
| #20260948 | 2 |
| #20260938 | 2 |
| #20260763 | 2 |
| #20260745 | 2 |
| #20260731 | 2 |
| C2×AGL(1,ℤ/8)×C97 | 2 |
| #3042 | 97 |