Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
160 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 85 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. #20260513 | C2 | semidirect |
| 4. #20260512 | C2 | semidirect |
| 5. #347×C97 | C2 | semidirect |
| 10. #15690749 | C4 | semidirect |
| 11. C16×D97 | C4 | semidirect |
| 55. C97 | #2110 | semidirect |
| 60. #347 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| M32×D97 | 2 |
| #20260692 | 2 |
| #20260513 | 2 |
| #20260512 | 2 |
| #347×C97 | 2 |
| #2110 | 97 |