Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
466 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 145 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. #20261533 | C2 | semidirect |
| 2. C2×#15690838 | C2 | semidirect |
| 3. C2×#15690835 | C2 | semidirect |
| 4. #20261005 | C2 | semidirect |
| 5. #20260998 | C2 | semidirect |
| 6. #20260784 | C2 | semidirect |
| 7. #20260717 | C2 | semidirect |
| 8. C2×#15690726 | C2 | semidirect |
| 9. #568×C97 | C2 | semidirect |
| 13. #15690840 | C22 | semidirect |
| 19. #15690835 | C22 | semidirect |
| 21. C2×#13095500 | C22 | semidirect |
| 23. C2×D776 | C22 | semidirect |
| 27. #15690746 | C22 | semidirect |
| 28. #15690728 | C22 | semidirect |
| 29. #15690726 | C22 | semidirect |
| 30. #15690726 | C22 | semidirect |
| 33. #131×C97 | C22 | semidirect |
| 148. C97 | #3068 | semidirect |
| 152. #568 | D97 | semidirect |
| 175. #131 | C2×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261533 | 2 |
| C2×#15690838 | 2 |
| C2×#15690835 | 2 |
| #20261005 | 2 |
| #20260998 | 2 |
| #20260784 | 2 |
| #20260717 | 2 |
| C2×#15690726 | 2 |
| #568×C97 | 2 |
| #3068 | 97 |