Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
272 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 72. C4×C97 | #101 | semidirect |
| 84. C97 | #1801 | semidirect |
| 161. C4 | #15690871 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261738 | 2 |
| C2×#15690871 | 2 |
| #20261615 | 2 |
| C2×C4×Dic194 | 2 |
| #1801 | 97 |