Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 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. C2×#15690836 | C2 | semidirect |
| 2. #20261302 | C2 | semidirect |
| 3. #20261210 | C2 | semidirect |
| 4. #20260948 | C2 | semidirect |
| 5. #20260928 | C2 | semidirect |
| 6. #20260761 | C2 | semidirect |
| 7. #20260740 | C2 | semidirect |
| 8. #20260732 | C2 | semidirect |
| 9. C22×D8×C97 | C2 | semidirect |
| 12. C2×#13095499 | C22 | semidirect |
| 13. C2×#13095496 | C22 | semidirect |
| 15. #15690806 | C22 | semidirect |
| 16. #15690797 | C22 | semidirect |
| 20. D4×Dic97 | C22 | semidirect |
| 24. #15690739 | C22 | semidirect |
| 25. #15690735 | C22 | semidirect |
| 26. #15690732 | C22 | semidirect |
| 27. #15690731 | C22 | semidirect |
| 60. C2×D4×C97 | D4 | semidirect |
| 122. C97 | #3041 | semidirect |
| 124. C22×D8 | D97 | semidirect |
| 168. C2×D4 | C22⋊D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690836 | 2 |
| #20261302 | 2 |
| #20261210 | 2 |
| #20260948 | 2 |
| #20260928 | 2 |
| #20260761 | 2 |
| #20260740 | 2 |
| #20260732 | 2 |
| C22×D8×C97 | 2 |
| #3041 | 97 |