Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
1464 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1464 conjugacy classes of subgroups — too many to draw. Only its 565 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. C23×Dic194 | C2 | semidirect |
| 3. C2×#15690843 | C2 | direct (N × H) |
| 4. C22×Dic388 | C2 | semidirect |
| 5. C22×#13095500 | C2 | semidirect |
| 6. C22×M16×C97 | C2 | semidirect |
| 13. C22×Dic194 | C22 | semidirect |
| 18. #15690843 | C22 | direct (N × H) |
| 19. C2×Dic388 | C22 | semidirect |
| 20. C2×#13095500 | C22 | semidirect |
| 22. C2×M16×C97 | C22 | semidirect |
| 33. C2×Dic194 | C23 | semidirect |
| 41. Dic388 | C23 | semidirect |
| 42. #13095500 | C23 | semidirect |
| 48. M16×C97 | C23 | semidirect |
| 74. C22×C97 | #137 | semidirect |
| 85. C2×C97 | C2×#137 | semidirect |
| 89. C97 | C22×#137 | semidirect |
| 95. C22×M16 | D97 | semidirect |
| 111. C2×M16 | C2×D97 | semidirect |
| 137. M16 | C22×D97 | semidirect |
| 165. C22 | #15690843 | direct (N × H) |
| 175. C2 | C2×#15690843 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095511 | 2 |
| C23×Dic194 | 2 |
| C2×#15690843 | 2 |
| C22×Dic388 | 2 |
| C22×#13095500 | 2 |
| C22×M16×C97 | 2 |
| C22×#137 | 97 |