Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
188 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 61 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. #20261015 | C2 | semidirect |
| 4. #20260486 | C2 | semidirect |
| 5. #20260482 | C2 | semidirect |
| 6. #20260478 | C2 | semidirect |
| 7. C8×D4×C97 | C2 | semidirect |
| 46. D4×C97 | SD16 | semidirect |
| 63. C8×C97 | D8 | semidirect |
| 86. C97 | #1665 | semidirect |
| 90. C8×D4 | D97 | semidirect |
| 139. D4 | #13095500 | semidirect |
| 151. C8 | #13095496 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261108 | 2 |
| #20261015 | 2 |
| #20260930 | 2 |
| #20260486 | 2 |
| #20260482 | 2 |
| #20260478 | 2 |
| C8×D4×C97 | 2 |
| #1665 | 97 |