Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
166 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 67 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. #20260485 | C2 | semidirect |
| 4. Q8⋊#11715895 | C2 | semidirect |
| 6. C8×#11715895 | C2 | semidirect |
| 7. #446×C97 | C2 | semidirect |
| 56. C8×C97 | SD16 | semidirect |
| 60. #11715895 | M16 | semidirect |
| 78. C97 | #1590 | semidirect |
| 79. #446 | D97 | semidirect |
| 138. C8 | #13095498 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13095498 | 2 |
| #20260814 | 2 |
| #20260485 | 2 |
| Q8⋊#11715895 | 2 |
| #20260462 | 2 |
| C8×#11715895 | 2 |
| #446×C97 | 2 |
| #1590 | 97 |