Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
756 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 209 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 |
|---|---|---|
| 2. #20261501 | C2 | semidirect |
| 3. #20260719 | C2 | semidirect |
| 4. #20260718 | C2 | semidirect |
| 5. C2×#15690726 | C2 | semidirect |
| 6. #100×D97 | C2 | semidirect |
| 7. #413×C97 | C2 | semidirect |
| 19. C2×#13095495 | C22 | semidirect |
| 20. M16×D97 | C22 | semidirect |
| 21. #15690729 | C22 | semidirect |
| 22. #15690727 | C22 | semidirect |
| 23. #15690726 | C22 | semidirect |
| 25. C2×M16×C97 | C22 | semidirect |
| 26. #101×C97 | C22 | semidirect |
| 27. #100×C97 | C22 | semidirect |
| 121. C97 | #2888 | semidirect |
| 126. #413 | D97 | semidirect |
| 143. C2×M16 | C2×D97 | semidirect |
| 145. #101 | C2×D97 | semidirect |
| 148. #100 | C2×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690856 | 2 |
| #20261501 | 2 |
| #20260719 | 2 |
| #20260718 | 2 |
| C2×#15690726 | 2 |
| #100×D97 | 2 |
| #413×C97 | 2 |
| #2888 | 97 |