Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
388 conjugacy classes of subgroups; only the 241 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 241 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. #20260866 | C2 | semidirect |
| 2. Q8×#11715895 | C2 | semidirect |
| 20. #13095495 | Q8 | direct (N × H) |
| 38. Q8×C97 | M16 | semidirect |
| 50. #11715895 | C2×Q8 | semidirect |
| 67. C97 | Q8×M16 | semidirect |
| 105. Q8 | #13095495 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20260866 | 2 |
| Q8×#11715895 | 2 |
| #20260759 | 2 |
| C4×#13095495 | 2 |
| C2×C4×Q8×C97 | 2 |
| Q8×M16 | 97 |