Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
500 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 197 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×#13095511 | C2 | semidirect |
| 3. C4×Dic388 | C2 | semidirect |
| 4. C4×#13095500 | C2 | semidirect |
| 5. C4×D776 | C2 | semidirect |
| 6. #20260773 | C2 | semidirect |
| 7. #20260732 | C2 | semidirect |
| 8. C2×C4×C8×C97 | C2 | semidirect |
| 10. #15690832 | C4 | direct (N × H) |
| 30. #13095511 | C2×C4 | semidirect |
| 36. Dic388 | C2×C4 | semidirect |
| 37. #13095500 | C2×C4 | semidirect |
| 38. D776 | C2×C4 | semidirect |
| 48. C2×C8×C97 | C2×C4 | semidirect |
| 83. C4×C97 | #135 | semidirect |
| 93. C97 | C4×#135 | semidirect |
| 101. C2×C4×C8 | D97 | semidirect |
| 135. C2×C8 | C4×D97 | semidirect |
| 178. C4 | #15690832 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690832 | 2 |
| C4×#13095511 | 2 |
| C4×Dic388 | 2 |
| C4×#13095500 | 2 |
| C4×D776 | 2 |
| #20260773 | 2 |
| #20260732 | 2 |
| C2×C4×C8×C97 | 2 |
| C4×#135 | 97 |