Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
648 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 173 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. C2×C4×D388 | C2 | semidirect |
| 4. #20260931 | C2 | direct (N × H) |
| 5. C2×#15690732 | C2 | semidirect |
| 6. C2×C4⋊C8×C97 | C2 | semidirect |
| 13. C2×D776 | C22 | semidirect |
| 15. #15690807 | C22 | semidirect |
| 17. C4×D388 | C22 | semidirect |
| 20. #15690732 | C22 | semidirect |
| 23. C4⋊C8×C97 | C22 | semidirect |
| 35. C2×D388 | D4 | semidirect |
| 62. C2×C4×C97 | D8 | semidirect |
| 78. D388 | C2×D4 | semidirect |
| 95. C4×C97 | C2×D8 | semidirect |
| 99. C2×C97 | #459 | semidirect |
| 106. C97 | C2×#459 | semidirect |
| 111. C2×C4⋊C8 | D97 | semidirect |
| 128. C4⋊C8 | C2×D97 | semidirect |
| 179. C2×C4 | D776 | semidirect |
| 202. C4 | C2×D776 | semidirect |
| 207. C2 | #20260931 | 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 |
| C2×C4×D388 | 2 |
| #20260931 | 2 |
| C2×#15690732 | 2 |
| C2×C4⋊C8×C97 | 2 |
| C2×#459 | 97 |