Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
752 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 165 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×#15690840 | C2 | semidirect |
| 2. C22×#13095499 | C2 | semidirect |
| 3. #20261306 | C2 | semidirect |
| 4. #20260897 | C2 | semidirect |
| 5. #20260886 | C2 | semidirect |
| 6. #20260740 | C2 | semidirect |
| 7. #20260731 | C2 | semidirect |
| 8. #20260702 | C2 | semidirect |
| 10. C22×Dic194 | C22 | semidirect |
| 12. C2×#13095501 | C22 | semidirect |
| 14. C2×#13095499 | C22 | semidirect |
| 15. C2×#13095499 | C22 | semidirect |
| 16. C2×#13095495 | C22 | semidirect |
| 17. C22×#11715895 | C22 | semidirect |
| 21. #15690789 | C22 | semidirect |
| 22. #15690769 | C22 | semidirect |
| 23. #15690734 | C22 | semidirect |
| 24. #15690731 | C22 | semidirect |
| 25. #15690731 | C22 | semidirect |
| 26. C22⋊#11715895 | C22 | semidirect |
| 147. C97 | #3009 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690840 | 2 |
| C22×#13095499 | 2 |
| #20261306 | 2 |
| #20260897 | 2 |
| #20260886 | 2 |
| #20260740 | 2 |
| #20260731 | 2 |
| #20260702 | 2 |
| C2×H(5,𝔽2)×C97 | 2 |
| #3009 | 97 |