Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
166 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 166 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 |
|---|---|---|
| 3. Q8×#11715895 | C2 | semidirect |
| 4. #20260487 | C2 | semidirect |
| 5. #20260481 | C2 | semidirect |
| 7. #462×C97 | C2 | semidirect |
| 79. C97 | #1682 | semidirect |
| 81. #462 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261083 | 2 |
| #20260935 | 2 |
| Q8×#11715895 | 2 |
| #20260487 | 2 |
| #20260481 | 2 |
| #20260478 | 2 |
| #462×C97 | 2 |
| #1682 | 97 |