Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
856 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 856 conjugacy classes of subgroups — too many to draw. Only its 218 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×#13095521 | C2 | semidirect |
| 2. C22×C4×#87604 | C2 | semidirect |
| 3. C2×#15690874 | C2 | direct (N × H) |
| 7. C2×#13095521 | C22 | semidirect |
| 10. C2×C4×#87604 | C22 | semidirect |
| 11. #15690874 | C22 | direct (N × H) |
| 14. C2×#13095510 | C4 | semidirect |
| 16. C22×Dic194 | C4 | semidirect |
| 20. C22×D4×C97 | C4 | semidirect |
| 24. #13095521 | C23 | semidirect |
| 27. C4×#87604 | C23 | semidirect |
| 32. #13095510 | C2×C4 | semidirect |
| 35. C2×Dic194 | C2×C4 | semidirect |
| 48. C2×D4×C97 | C2×C4 | semidirect |
| 59. D4×C97 | C22×C4 | semidirect |
| 75. Dic194 | C22×C4 | semidirect |
| 79. C22×C97 | #104 | semidirect |
| 92. C2×C97 | C2×#104 | semidirect |
| 97. C97 | C22×#104 | semidirect |
| 108. C22×D4 | #87604 | semidirect |
| 130. C2×D4 | C2×#87604 | semidirect |
| 158. D4 | C22×#87604 | semidirect |
| 180. C22 | #15690874 | direct (N × H) |
| 191. C2 | C2×#15690874 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095521 | 2 |
| C22×C4×#87604 | 2 |
| C2×#15690874 | 2 |
| C22×#13095510 | 2 |
| C22×#104 | 97 |