Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
1168 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 1168 conjugacy classes of subgroups — too many to draw. Only its 209 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×#13095488 | C2 | semidirect |
| 3. C2×#15690717 | C2 | semidirect |
| 4. C2×#95×C97 | C2 | semidirect |
| 9. C22×D388 | C4 | semidirect |
| 35. C22×Dic97 | D4 | semidirect |
| 46. C22×C4×C97 | D4 | semidirect |
| 75. C22×D97 | C22⋊C4 | semidirect |
| 84. C2×C4×C97 | C22⋊C4 | semidirect |
| 129. C97 | #1438 | semidirect |
| 133. C2×#95 | D97 | semidirect |
| 173. C22×C4 | D388 | semidirect |
| 219. C2×C4 | #13095488 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D388 | 2 |
| C22×#13095488 | 2 |
| C2×#15690717 | 2 |
| C2×#95×C97 | 2 |
| #1438 | 97 |