Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
616 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 616 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×D776 | C2 | semidirect |
| 2. C22×C8×D97 | C2 | semidirect |
| 3. C2×#15690785 | C2 | semidirect |
| 4. #20260972 | C2 | direct (N × H) |
| 5. C2×#15690730 | C2 | semidirect |
| 6. C2×#107×C97 | C2 | semidirect |
| 11. C2×D776 | C22 | semidirect |
| 14. C2×C8×D97 | C22 | semidirect |
| 16. #15690785 | C22 | semidirect |
| 18. #15690730 | C22 | semidirect |
| 21. #107×C97 | C22 | semidirect |
| 42. C2×C8×C97 | D4 | semidirect |
| 53. C22×D97 | D8 | semidirect |
| 70. C8×C97 | C2×D4 | semidirect |
| 83. C2×D97 | C2×D8 | semidirect |
| 89. C2×C97 | #466 | semidirect |
| 96. C97 | C2×#466 | semidirect |
| 101. C2×#107 | D97 | semidirect |
| 116. #107 | C2×D97 | semidirect |
| 137. C2×C8 | D388 | semidirect |
| 167. C8 | C2×D388 | semidirect |
| 187. C2 | #20260972 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D776 | 2 |
| C22×C8×D97 | 2 |
| C2×#15690785 | 2 |
| #20260972 | 2 |
| C2×#15690730 | 2 |
| C2×#107×C97 | 2 |
| C2×#466 | 97 |