Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
384 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 117 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×#15690744 | C2 | semidirect |
| 3. C2×#15690732 | C2 | semidirect |
| 4. #20260637 | C2 | semidirect |
| 5. C2×C4×C8×C97 | C2 | semidirect |
| 9. C2×D776 | C4 | semidirect |
| 48. C2×C4×C97 | D8 | semidirect |
| 62. C8×C97 | C22⋊C4 | semidirect |
| 86. C97 | #1970 | semidirect |
| 90. C2×C4×C8 | D97 | semidirect |
| 140. C2×C4 | D776 | semidirect |
| 148. C8 | #13095488 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D776 | 2 |
| C2×#15690744 | 2 |
| C2×#15690732 | 2 |
| #20260637 | 2 |
| C2×C4×C8×C97 | 2 |
| #1970 | 97 |