Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
228 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 65 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. #20260484 | C2 | semidirect |
| 4. Q8⋊#11715895 | C2 | semidirect |
| 5. Q82×C97 | C2 | semidirect |
| 37. Q8×C97 | SD16 | semidirect |
| 61. C97 | #1623 | semidirect |
| 62. Q82 | D97 | semidirect |
| 98. 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 |
| #20260484 | 2 |
| Q8⋊#11715895 | 2 |
| Q82×C97 | 2 |
| #1623 | 97 |