Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
174 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 65 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. C4×D776 | C2 | semidirect |
| 3. #20260560 | C2 | semidirect |
| 4. #20260536 | C2 | semidirect |
| 5. #20260535 | C2 | semidirect |
| 6. C4×#13095486 | C2 | semidirect |
| 7. C4×D8×C97 | C2 | semidirect |
| 10. #15690751 | C4 | direct (N × H) |
| 23. D776 | C2×C4 | semidirect |
| 27. #13095486 | C2×C4 | semidirect |
| 31. D8×C97 | C2×C4 | semidirect |
| 62. C4×C97 | D16 | semidirect |
| 72. C97 | C4×D16 | semidirect |
| 75. C4×D8 | D97 | semidirect |
| 99. D8 | C4×D97 | semidirect |
| 135. C4 | #15690751 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690751 | 2 |
| C4×D776 | 2 |
| #20260560 | 2 |
| #20260536 | 2 |
| #20260535 | 2 |
| C4×#13095486 | 2 |
| C4×D8×C97 | 2 |
| C4×D16 | 97 |