Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
168 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 55 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. #20261017 | C2 | semidirect |
| 3. #20260865 | C2 | semidirect |
| 4. #20260488 | C2 | semidirect |
| 5. #20260481 | C2 | semidirect |
| 59. C8×C97 | SD16 | semidirect |
| 80. C97 | #1686 | semidirect |
| 142. C8 | #13095499 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261017 | 2 |
| #20260932 | 2 |
| #20260865 | 2 |
| #20260488 | 2 |
| #20260481 | 2 |
| #20260479 | 2 |
| #492×C97 | 2 |
| #1686 | 97 |