Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
210 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 210 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 |
|---|---|---|
| 1. #20261464 | C2 | semidirect |
| 5. #20260482 | C2 | semidirect |
| 6. #20260467 | C2 | semidirect |
| 7. Q8⋊C8×C97 | C2 | semidirect |
| 51. Q8×C97 | SD16 | semidirect |
| 91. C97 | #1626 | semidirect |
| 98. Q8⋊C8 | D97 | semidirect |
| 146. Q8 | #13095500 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261464 | 2 |
| #20261082 | 2 |
| #20260936 | 2 |
| #20260935 | 2 |
| #20260482 | 2 |
| #20260467 | 2 |
| Q8⋊C8×C97 | 2 |
| #1626 | 97 |