Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
588 conjugacy classes of subgroups; only the 277 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 277 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. #15690810 | C4 | direct (N × H) |
| 41. C42×C97 | Q8 | semidirect |
| 70. C4×C97 | C4×Q8 | semidirect |
| 71. C4×C97 | C4⋊Q8 | semidirect |
| 80. C97 | C4×C4⋊Q8 | semidirect |
| 119. C42 | Dic194 | semidirect |
| 152. C4 | C4×Dic194 | semidirect |
| 153. C4 | #15690810 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690810 | 2 |
| C2×C4×Dic194 | 2 |
| #20260641 | 2 |
| #20260633 | 2 |
| #20260605 | 2 |
| C4×C4⋊Dic97 | 2 |
| C43×C97 | 2 |
| C4×C4⋊Q8 | 97 |