Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
608 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 197 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 |
|---|---|---|
| 2. C2×#15690772 | C2 | semidirect |
| 3. #20260846 | C2 | direct (N × H) |
| 4. C2×#15690730 | C2 | semidirect |
| 5. C2×#15690720 | C2 | semidirect |
| 6. C2×#106×C97 | C2 | semidirect |
| 9. C2×D776 | C4 | semidirect |
| 13. #15690772 | C22 | semidirect |
| 16. #15690730 | C22 | semidirect |
| 17. #15690720 | C22 | semidirect |
| 20. #106×C97 | C22 | semidirect |
| 24. C2×D388 | C2×C4 | semidirect |
| 29. D776 | C2×C4 | semidirect |
| 37. C2×C8×C97 | C2×C4 | semidirect |
| 56. D388 | C22×C4 | semidirect |
| 58. C8×C97 | C22×C4 | semidirect |
| 72. C2×C97 | #442 | semidirect |
| 77. C97 | C2×#442 | semidirect |
| 81. C2×#106 | D97 | semidirect |
| 95. #106 | C2×D97 | semidirect |
| 111. C2×C8 | C4×D97 | semidirect |
| 136. C8 | C2×C4×D97 | semidirect |
| 150. C2 | #20260846 | 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×#15690772 | 2 |
| #20260846 | 2 |
| C2×#15690730 | 2 |
| C2×#15690720 | 2 |
| C2×#106×C97 | 2 |
| C2×#442 | 97 |