Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
154 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 53 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. #20260858 | C2 | semidirect |
| 3. #20260848 | C2 | semidirect |
| 4. #20260558 | C2 | semidirect |
| 5. #20260549 | C2 | semidirect |
| 6. #20260546 | C2 | semidirect |
| 7. #347×C97 | C2 | semidirect |
| 12. #15690755 | C4 | semidirect |
| 13. D1552 | C4 | semidirect |
| 24. Dic388 | C2×C4 | semidirect |
| 28. D776 | C2×C4 | semidirect |
| 38. C16×C97 | C2×C4 | semidirect |
| 69. C97 | AGL(1,ℤ/16) | semidirect |
| 76. #347 | D97 | semidirect |
| 107. C16 | C4×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261173 | 2 |
| #20260858 | 2 |
| #20260848 | 2 |
| #20260558 | 2 |
| #20260549 | 2 |
| #20260546 | 2 |
| #347×C97 | 2 |
| AGL(1,ℤ/16) | 97 |