Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
1048 conjugacy classes of subgroups; only the 573 normal subgroups are shown.
This group has 1048 conjugacy classes of subgroups — too many to draw. Only its 573 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. #20261461 | C2 | direct (N × H) |
| 42. C2×Q8×C97 | Q8 | semidirect |
| 50. Q8×C97 | C2×Q8 | semidirect |
| 77. C2×C97 | #557 | semidirect |
| 82. C97 | C2×#557 | semidirect |
| 112. C2×Q8 | Dic194 | semidirect |
| 133. Q8 | C2×Dic194 | semidirect |
| 159. C2 | #20261461 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261461 | 2 |
| C2×#15690809 | 2 |
| C2×#15690802 | 2 |
| C2×#15690801 | 2 |
| C2×Q8×Dic97 | 2 |
| C2×C4×Dic194 | 2 |
| C2×C4×Q8×C97 | 2 |
| C2×#557 | 97 |