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×#13095512 | C2 | semidirect |
| 2. C22×#13095498 | C2 | semidirect |
| 3. C22×D776 | C2 | semidirect |
| 4. C2×#15690785 | C2 | semidirect |
| 5. #20260883 | C2 | direct (N × H) |
| 6. C2×#15690730 | C2 | semidirect |
| 7. C2×#15690722 | C2 | semidirect |
| 8. C2×#103×C97 | C2 | semidirect |
| 12. C2×#13095512 | C22 | semidirect |
| 20. C2×#13095498 | C22 | semidirect |
| 22. C2×D776 | C22 | semidirect |
| 25. #15690785 | C22 | semidirect |
| 27. #15690730 | C22 | semidirect |
| 28. #15690722 | C22 | semidirect |
| 32. #103×C97 | C22 | semidirect |
| 48. C2×D388 | D4 | semidirect |
| 65. C2×Q8×C97 | D4 | semidirect |
| 89. Q8×C97 | C2×D4 | semidirect |
| 107. D388 | C2×D4 | semidirect |
| 136. C2×C97 | #449 | semidirect |
| 144. C97 | C2×#449 | semidirect |
| 150. C2×#103 | D97 | semidirect |
| 174. #103 | C2×D97 | semidirect |
| 185. C2×Q8 | D388 | semidirect |
| 233. Q8 | C2×D388 | semidirect |
| 283. C2 | #20260883 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095512 | 2 |
| C22×#13095498 | 2 |
| C22×D776 | 2 |
| C2×#15690785 | 2 |
| #20260883 | 2 |
| C2×#15690730 | 2 |
| C2×#15690722 | 2 |
| C2×#103×C97 | 2 |
| C2×#449 | 97 |