Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
172 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 172 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 |
|---|---|---|
| 3. Q8×#11715895 | C2 | semidirect |
| 4. #20260485 | C2 | semidirect |
| 5. #20260481 | C2 | semidirect |
| 7. #475×C97 | C2 | semidirect |
| 46. Q8×C97 | SD16 | semidirect |
| 62. #11715895 | SD16 | semidirect |
| 80. C97 | #1666 | semidirect |
| 82. #475 | D97 | semidirect |
| 126. Q8 | #13095498 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261109 | 2 |
| #20260935 | 2 |
| Q8×#11715895 | 2 |
| #20260485 | 2 |
| #20260481 | 2 |
| #20260478 | 2 |
| #475×C97 | 2 |
| #1666 | 97 |