Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
188 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 57 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. #20261108 | C2 | semidirect |
| 2. #20261016 | C2 | semidirect |
| 4. C8×D388 | C2 | semidirect |
| 5. #20260480 | C2 | semidirect |
| 6. #20260478 | C2 | semidirect |
| 7. #334×C97 | C2 | semidirect |
| 56. D388 | SD16 | semidirect |
| 64. C8×C97 | D8 | semidirect |
| 86. C97 | #1665 | semidirect |
| 91. #334 | D97 | semidirect |
| 151. C8 | D776 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261108 | 2 |
| #20261016 | 2 |
| #20260931 | 2 |
| C8×D388 | 2 |
| #20260480 | 2 |
| #20260478 | 2 |
| #334×C97 | 2 |
| #1665 | 97 |