Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
446 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 137 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. C2×#15690841 | C2 | semidirect |
| 3. #20261502 | C2 | semidirect |
| 4. #20261008 | C2 | semidirect |
| 5. #20261000 | C2 | semidirect |
| 6. #20260783 | C2 | semidirect |
| 7. #20260717 | C2 | semidirect |
| 8. C2×#15690729 | C2 | semidirect |
| 9. C2×#137×C97 | C2 | semidirect |
| 18. C2×#13095501 | C22 | semidirect |
| 19. C2×#13095498 | C22 | semidirect |
| 26. #15690745 | C22 | semidirect |
| 27. #15690729 | C22 | semidirect |
| 28. #15690728 | C22 | semidirect |
| 29. #15690726 | C22 | semidirect |
| 143. C97 | #3069 | semidirect |
| 146. C2×#137 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261533 | 2 |
| C2×#15690841 | 2 |
| #20261502 | 2 |
| #20261008 | 2 |
| #20261000 | 2 |
| #20260783 | 2 |
| #20260717 | 2 |
| C2×#15690729 | 2 |
| C2×#137×C97 | 2 |
| #3069 | 97 |