Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
596 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 149 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×#15690835 | C2 | semidirect |
| 2. C22×D776 | C2 | semidirect |
| 3. #20261299 | C2 | semidirect |
| 4. #20261121 | C2 | semidirect |
| 5. #20261120 | C2 | semidirect |
| 6. #20261110 | C2 | semidirect |
| 7. #20260690 | C2 | semidirect |
| 8. C2×#135×C97 | C2 | semidirect |
| 11. C2×#13095498 | C22 | semidirect |
| 15. C2×#13095496 | C22 | semidirect |
| 17. #15690806 | C22 | semidirect |
| 18. #15690799 | C22 | semidirect |
| 22. #15690720 | C22 | semidirect |
| 23. C8×Dic97 | C22 | semidirect |
| 26. C2×Q16×C97 | C22 | semidirect |
| 27. C2×SD16×C97 | C22 | semidirect |
| 28. C2×D8×C97 | C22 | semidirect |
| 40. #13095495 | D4 | semidirect |
| 56. C2×C8×C97 | D4 | semidirect |
| 102. C97 | #3155 | semidirect |
| 104. C2×#135 | D97 | semidirect |
| 115. C2×Q16 | C2×D97 | semidirect |
| 117. C2×SD16 | C2×D97 | semidirect |
| 122. C2×D8 | C2×D97 | semidirect |
| 154. C2×C8 | C22⋊D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690835 | 2 |
| C22×D776 | 2 |
| #20261299 | 2 |
| #20261121 | 2 |
| #20261120 | 2 |
| #20261110 | 2 |
| #20260690 | 2 |
| C2×#135×C97 | 2 |
| #3155 | 97 |