Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
568 conjugacy classes of subgroups; only the 287 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 287 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 |
|---|---|---|
| 9. Q8×Dic97 | C4 | semidirect |
| 31. #13095490 | Q8 | direct (N × H) |
| 43. Q8×C97 | C4⋊C4 | semidirect |
| 78. Dic97 | C4×Q8 | semidirect |
| 87. C97 | Q8×C4⋊C4 | semidirect |
| 130. Q8 | #13095490 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×Dic97 | 2 |
| #20260633 | 2 |
| #20260631 | 2 |
| #20260604 | 2 |
| C4×#13095490 | 2 |
| C2×C4×Q8×C97 | 2 |
| Q8×C4⋊C4 | 97 |