Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
466 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 466 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. #20261533 | C2 | semidirect |
| 2. C2×#15690838 | C2 | semidirect |
| 3. C2×#15690835 | C2 | semidirect |
| 4. #20261501 | C2 | semidirect |
| 5. #20261004 | C2 | semidirect |
| 6. #20261001 | C2 | semidirect |
| 7. #20260783 | C2 | semidirect |
| 8. C2×#15690726 | C2 | semidirect |
| 9. #413×C97 | C2 | semidirect |
| 12. #15690841 | C22 | semidirect |
| 16. #15690836 | C22 | semidirect |
| 22. C2×#13095498 | C22 | semidirect |
| 24. C2×#13095496 | C22 | semidirect |
| 25. #15690818 | C22 | semidirect |
| 30. #15690745 | C22 | semidirect |
| 31. #15690726 | C22 | semidirect |
| 35. #101×C97 | C22 | semidirect |
| 36. #100×C97 | C22 | semidirect |
| 148. C97 | #3068 | semidirect |
| 156. #413 | D97 | semidirect |
| 182. #101 | C2×D97 | semidirect |
| 184. #100 | 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 |
| #20261501 | 2 |
| #20261004 | 2 |
| #20261001 | 2 |
| #20260783 | 2 |
| C2×#15690726 | 2 |
| #413×C97 | 2 |
| #3068 | 97 |