Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
760 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 213 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. C2×#15690807 | C2 | semidirect |
| 3. #20261112 | C2 | direct (N × H) |
| 4. C2×C4×C8×C97 | C2 | semidirect |
| 8. C2×D776 | C22 | semidirect |
| 10. #15690807 | C22 | semidirect |
| 13. C4×C8×C97 | C22 | semidirect |
| 23. C2×C8×C97 | D4 | semidirect |
| 31. C2×C4×C97 | D8 | semidirect |
| 39. C8×C97 | C2×D4 | semidirect |
| 47. C4×C97 | C2×D8 | semidirect |
| 49. C2×C97 | #493 | semidirect |
| 54. C97 | C2×#493 | semidirect |
| 58. C2×C4×C8 | D97 | semidirect |
| 67. C4×C8 | C2×D97 | semidirect |
| 77. C2×C8 | D388 | semidirect |
| 88. C2×C4 | D776 | semidirect |
| 93. C8 | C2×D388 | semidirect |
| 101. C4 | C2×D776 | semidirect |
| 104. C2 | #20261112 | 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 |
| C2×#15690807 | 2 |
| #20261112 | 2 |
| C2×C4×C8×C97 | 2 |
| C2×#493 | 97 |