Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
552 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 221 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. C2×C4×Dic194 | C2 | semidirect |
| 4. C4×#13095500 | C2 | direct (N × H) |
| 5. C2×#15690742 | C2 | semidirect |
| 6. C2×#15690735 | C2 | semidirect |
| 8. C2×C4×C8×C97 | C2 | semidirect |
| 12. C2×#13095500 | C4 | direct (N × H) |
| 15. C4×Dic194 | C22 | semidirect |
| 23. #15690742 | C22 | semidirect |
| 24. #15690735 | C22 | semidirect |
| 29. C4×C8×C97 | C22 | semidirect |
| 33. C2×Dic194 | C2×C4 | semidirect |
| 44. #13095500 | C2×C4 | direct (N × H) |
| 56. C2×C8×C97 | C2×C4 | semidirect |
| 67. C2×C4×C97 | SD16 | semidirect |
| 86. Dic194 | C22×C4 | semidirect |
| 88. C8×C97 | C22×C4 | semidirect |
| 99. C4×C97 | C2×SD16 | semidirect |
| 105. C2×C97 | C4×SD16 | semidirect |
| 111. C97 | C2×C4×SD16 | semidirect |
| 119. C2×C4×C8 | D97 | semidirect |
| 140. C4×C8 | C2×D97 | semidirect |
| 160. C2×C8 | C4×D97 | semidirect |
| 191. C2×C4 | #13095500 | direct (N × H) |
| 199. C8 | C2×C4×D97 | semidirect |
| 213. C4 | C2×#13095500 | direct (N × H) |
| 217. C2 | C4×#13095500 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095500 | 2 |
| C2×C4×Dic194 | 2 |
| C2×C4×D388 | 2 |
| C4×#13095500 | 2 |
| C2×#15690742 | 2 |
| C2×#15690735 | 2 |
| C2×#15690732 | 2 |
| C2×C4×C8×C97 | 2 |
| C2×C4×SD16 | 97 |