Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
812 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 812 conjugacy classes of subgroups — too many to draw. Only its 165 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×#13095511 | C2 | semidirect |
| 2. C22×#13095499 | C2 | semidirect |
| 3. C22×#13095496 | C2 | semidirect |
| 4. #20260878 | C2 | direct (N × H) |
| 5. C2×#15690733 | C2 | semidirect |
| 6. C2×#15690730 | C2 | semidirect |
| 7. C2×C22⋊#11715895 | C2 | semidirect |
| 8. C2×#121×C97 | C2 | semidirect |
| 12. C2×#13095511 | C22 | semidirect |
| 18. C2×#13095499 | C22 | semidirect |
| 20. C2×#13095496 | C22 | semidirect |
| 23. #15690733 | C22 | semidirect |
| 24. #15690730 | C22 | semidirect |
| 25. C22⋊#11715895 | C22 | semidirect |
| 30. #121×C97 | C22 | semidirect |
| 39. C2×Dic194 | D4 | semidirect |
| 43. C2×D388 | D4 | semidirect |
| 107. D388 | C2×D4 | semidirect |
| 111. Dic194 | C2×D4 | semidirect |
| 138. C2×C97 | #449 | semidirect |
| 144. C97 | C2×#449 | semidirect |
| 148. C2×#121 | D97 | semidirect |
| 171. #121 | C2×D97 | semidirect |
| 283. C2 | #20260878 | 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 |
| C22×#13095499 | 2 |
| C22×#13095496 | 2 |
| #20260878 | 2 |
| C2×#15690733 | 2 |
| C2×#15690730 | 2 |
| C2×C22⋊#11715895 | 2 |
| C2×#121×C97 | 2 |
| C2×#449 | 97 |