Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
438 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 103 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×C4×D388 | C2 | semidirect |
| 3. C2×#15690732 | C2 | semidirect |
| 4. C2×#15690732 | C2 | semidirect |
| 5. #20260637 | C2 | semidirect |
| 6. #20260498 | C2 | semidirect |
| 7. #336×C97 | C2 | semidirect |
| 13. C2×D776 | C4 | semidirect |
| 37. C2×D388 | C2×C4 | semidirect |
| 61. C2×C8×C97 | C2×C4 | semidirect |
| 84. C2×C4×C97 | D8 | semidirect |
| 104. D388 | C22⋊C4 | semidirect |
| 147. C97 | #1879 | semidirect |
| 154. #336 | D97 | semidirect |
| 201. C2×C8 | C4×D97 | semidirect |
| 246. C2×C4 | D776 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D776 | 2 |
| C2×C4×D388 | 2 |
| C2×#15690732 | 2 |
| #20260637 | 2 |
| #20260498 | 2 |
| #336×C97 | 2 |
| #1879 | 97 |