Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
404 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 135 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 |
|---|---|---|
| 3. #20260492 | C2 | semidirect |
| 4. #20260491 | C2 | semidirect |
| 5. H(3,ℤ/4)×C97 | C2 | semidirect |
| 8. C2×#13095494 | C4 | semidirect |
| 11. C2×C8×D97 | C4 | semidirect |
| 14. #15690767 | C4 | semidirect |
| 18. C42×D97 | C4 | semidirect |
| 34. C2×#11715895 | C2×C4 | semidirect |
| 42. C4×Dic97 | C2×C4 | semidirect |
| 45. C2×C8×C97 | C2×C4 | semidirect |
| 48. C42×C97 | C2×C4 | semidirect |
| 101. D97 | H(3,ℤ/4) | direct (N × H) |
| 103. C97 | C2×H(3,ℤ/4) | semidirect |
| 108. H(3,ℤ/4) | D97 | direct (N × H) |
| 142. C2×C8 | C4×D97 | semidirect |
| 151. C42 | C4×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×D97 | 2 |
| #117×D97 | 2 |
| #20260492 | 2 |
| #20260491 | 2 |
| H(3,ℤ/4)×C97 | 2 |
| C2×H(3,ℤ/4) | 97 |