Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
364 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 129 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×#15690832 | C2 | semidirect |
| 2. #20261176 | C2 | semidirect |
| 3. #20261175 | C2 | semidirect |
| 4. #20261171 | C2 | semidirect |
| 5. #20261170 | C2 | semidirect |
| 6. #20261165 | C2 | semidirect |
| 7. C2×#15690750 | C2 | semidirect |
| 8. C2×#135×C97 | C2 | semidirect |
| 13. #15690832 | C22 | semidirect |
| 14. C2×Dic388 | C22 | semidirect |
| 16. C2×D776 | C22 | semidirect |
| 17. #15690756 | C22 | semidirect |
| 18. #15690754 | C22 | semidirect |
| 19. #15690753 | C22 | semidirect |
| 20. #15690751 | C22 | semidirect |
| 21. #15690750 | C22 | semidirect |
| 22. #15690750 | C22 | semidirect |
| 23. C2×#13095486 | C22 | semidirect |
| 28. #135×C97 | C22 | semidirect |
| 29. C2×Q16×C97 | C22 | semidirect |
| 31. C2×D8×C97 | C22 | semidirect |
| 121. C97 | #3414 | semidirect |
| 123. C2×#135 | D97 | semidirect |
| 139. #135 | C2×D97 | semidirect |
| 141. C2×Q16 | C2×D97 | semidirect |
| 145. C2×D8 | C2×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690832 | 2 |
| #20261176 | 2 |
| #20261175 | 2 |
| #20261171 | 2 |
| #20261170 | 2 |
| #20261165 | 2 |
| C2×#15690750 | 2 |
| C2×#135×C97 | 2 |
| #3414 | 97 |