Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
596 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 157 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 |
|---|---|---|
| 1. C22×#13095494 | C2 | semidirect |
| 2. C2×#15690781 | C2 | semidirect |
| 3. #20260985 | C2 | direct (N × H) |
| 4. C2×#15690742 | C2 | semidirect |
| 5. C2×#15690731 | C2 | semidirect |
| 6. C22×D8×C97 | C2 | semidirect |
| 10. C2×#13095494 | C22 | semidirect |
| 13. #15690781 | C22 | semidirect |
| 16. #15690742 | C22 | semidirect |
| 17. #15690731 | C22 | semidirect |
| 20. C2×D8×C97 | C22 | semidirect |
| 44. C2×C8×C97 | D4 | semidirect |
| 69. C8×C97 | C2×D4 | semidirect |
| 87. C2×C97 | #469 | semidirect |
| 92. C97 | C2×#469 | semidirect |
| 93. C22×D8 | D97 | semidirect |
| 103. C2×D8 | C2×D97 | semidirect |
| 133. C2×C8 | C22⋊D97 | semidirect |
| 162. C8 | C2×C22⋊D97 | semidirect |
| 180. C2 | #20260985 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095494 | 2 |
| C2×#15690781 | 2 |
| #20260985 | 2 |
| C2×#15690742 | 2 |
| C2×#15690731 | 2 |
| C22×D8×C97 | 2 |
| C2×#469 | 97 |