Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
140 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 43 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 |
|---|---|---|
| 2. C22⋊#13095486 | C2 | semidirect |
| 3. C22⋊C16×C97 | C2 | semidirect |
| 30. C22×D97 | C16 | semidirect |
| 64. C97 | #1314 | semidirect |
| 67. C22⋊C16 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690722 | 2 |
| C22⋊#13095486 | 2 |
| C22⋊C16×C97 | 2 |
| #1314 | 97 |