Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
1880 conjugacy classes of subgroups; only the 901 normal subgroups are shown.
This group has 1880 conjugacy classes of subgroups — too many to draw. Only its 901 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. C2×#15690767 | C2 | direct (N × H) |
| 3. C22×#13095490 | C2 | semidirect |
| 5. C22×C4×Dic97 | C2 | semidirect |
| 6. C22×C42×C97 | C2 | semidirect |
| 10. C22×C4×D97 | C4 | semidirect |
| 12. #15690767 | C22 | direct (N × H) |
| 13. C2×#13095490 | C22 | semidirect |
| 15. C2×C4×Dic97 | C22 | semidirect |
| 18. C2×C42×C97 | C22 | semidirect |
| 26. C2×C4×D97 | C2×C4 | semidirect |
| 28. #13095490 | C23 | semidirect |
| 30. C4×Dic97 | C23 | semidirect |
| 36. C42×C97 | C23 | semidirect |
| 52. C4×D97 | C22×C4 | semidirect |
| 53. C22×C97 | #117 | semidirect |
| 64. C2×C97 | C2×#117 | semidirect |
| 69. C97 | C22×#117 | semidirect |
| 75. C22×C42 | D97 | semidirect |
| 87. C2×C42 | C2×D97 | semidirect |
| 105. C42 | C22×D97 | semidirect |
| 125. C22 | #15690767 | direct (N × H) |
| 134. C2 | C2×#15690767 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×D97 | 2 |
| C2×#15690767 | 2 |
| C22×#13095490 | 2 |
| C22×#13095488 | 2 |
| C22×C4×Dic97 | 2 |
| C22×C42×C97 | 2 |
| C22×#117 | 97 |