Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
492 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 200 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. #20261746 | C2 | semidirect |
| 3. #20261745 | C2 | semidirect |
| 12. #15690879 | C22 | semidirect |
| 13. #15690878 | C22 | semidirect |
| 15. C2×#13095495 | C4 | semidirect |
| 16. C2×#13095494 | C4 | semidirect |
| 17. M16×D97 | C4 | semidirect |
| 20. C2×M16×C97 | C4 | semidirect |
| 38. #13095495 | C2×C4 | semidirect |
| 39. #13095494 | C2×C4 | semidirect |
| 40. C2×#11715895 | C2×C4 | semidirect |
| 41. C8×D97 | C2×C4 | semidirect |
| 44. M16×C97 | C2×C4 | semidirect |
| 45. C2×C8×C97 | C2×C4 | semidirect |
| 98. C97 | #2911 | semidirect |
| 108. C2×M16 | #87604 | semidirect |
| 133. M16 | C2×#87604 | semidirect |
| 137. C2×C8 | C2×#87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690889 | 2 |
| #20261746 | 2 |
| #20261745 | 2 |
| C2×M16×D97 | 2 |
| #2911 | 97 |