Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
516 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 205 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. #20260619 | C2 | semidirect |
| 4. #20260603 | C2 | semidirect |
| 5. C4×#13095490 | C2 | semidirect |
| 7. C43×C97 | C2 | semidirect |
| 9. #15690804 | C4 | direct (N × H) |
| 28. #13095490 | C2×C4 | semidirect |
| 37. C42×C97 | C2×C4 | semidirect |
| 65. C4×C97 | #126 | semidirect |
| 74. C97 | C4×#126 | semidirect |
| 81. C43 | D97 | semidirect |
| 111. C42 | C4×D97 | semidirect |
| 142. C4 | #15690804 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690804 | 2 |
| #20260626 | 2 |
| #20260619 | 2 |
| #20260603 | 2 |
| C4×#13095490 | 2 |
| C4×#13095488 | 2 |
| C43×C97 | 2 |
| C4×#126 | 97 |