Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
484 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 189 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. #20261215 | C2 | semidirect |
| 3. #20260837 | C2 | semidirect |
| 4. C4×Dic388 | C2 | semidirect |
| 5. C4×D776 | C2 | semidirect |
| 6. C2×#15690744 | C2 | semidirect |
| 7. #20260737 | C2 | semidirect |
| 8. #405×C97 | C2 | semidirect |
| 10. #15690832 | C4 | semidirect |
| 30. #13095511 | C2×C4 | semidirect |
| 37. Dic388 | C2×C4 | semidirect |
| 38. #13095500 | C2×C4 | semidirect |
| 39. D776 | C2×C4 | semidirect |
| 47. C2×C8×C97 | C2×C4 | semidirect |
| 96. C97 | #2951 | semidirect |
| 104. #405 | D97 | semidirect |
| 138. C2×C8 | C4×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690832 | 2 |
| #20261215 | 2 |
| #20260837 | 2 |
| C4×Dic388 | 2 |
| C4×D776 | 2 |
| C2×#15690744 | 2 |
| #20260737 | 2 |
| #405×C97 | 2 |
| #2951 | 97 |