Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
412 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 99 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×#13095494 | C2 | semidirect |
| 3. C2×#15690732 | C2 | semidirect |
| 4. C2×#15690730 | C2 | semidirect |
| 5. #20260592 | C2 | semidirect |
| 6. #20260497 | C2 | semidirect |
| 7. #340×C97 | C2 | semidirect |
| 16. #15690785 | C4 | semidirect |
| 48. C2×#11715895 | D4 | semidirect |
| 58. C2×C8×C97 | D4 | semidirect |
| 146. C97 | #1895 | semidirect |
| 153. #340 | D97 | semidirect |
| 200. C2×C8 | D388 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095494 | 2 |
| C2×#15690785 | 2 |
| C2×#15690732 | 2 |
| C2×#15690730 | 2 |
| #20260592 | 2 |
| #20260497 | 2 |
| #340×C97 | 2 |
| #1895 | 97 |