Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
488 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 205 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 |
|---|---|---|
| 4. #20260827 | C2 | direct (N × H) |
| 10. C2×#13095501 | C4 | semidirect |
| 38. #13095501 | C2×C4 | semidirect |
| 77. C2×Dic97 | Q16 | semidirect |
| 97. Dic97 | C2×Q16 | semidirect |
| 98. C2×C97 | C4×Q16 | semidirect |
| 103. C97 | C2×C4×Q16 | semidirect |
| 201. C2 | #20260827 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095501 | 2 |
| C2×Q8×Dic97 | 2 |
| C2×#15690775 | 2 |
| #20260827 | 2 |
| C2×#15690743 | 2 |
| C2×#15690735 | 2 |
| C2×C8×Dic97 | 2 |
| C2×#103×C97 | 2 |
| C2×C4×Q16 | 97 |