Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
408 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 97 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. C2×#15690724 | C2 | semidirect |
| 3. #20260595 | C2 | semidirect |
| 4. C4×C22⋊C4×C97 | C2 | semidirect |
| 5. C22×D388 | C4 | semidirect |
| 12. C2×C4⋊Dic97 | C4 | semidirect |
| 14. C2×#13095488 | C4 | semidirect |
| 47. C22⋊C4×C97 | D4 | semidirect |
| 104. C4×C97 | #99 | semidirect |
| 116. C97 | #1964 | semidirect |
| 120. C4×C22⋊C4 | D97 | semidirect |
| 163. C22⋊C4 | D388 | semidirect |
| 222. C4 | #15690724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690784 | 2 |
| C2×#15690724 | 2 |
| #20260595 | 2 |
| C4×C22⋊C4×C97 | 2 |
| #1964 | 97 |