Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
212 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 212 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. #20261819 | C2 | semidirect |
| 3. C8×#11715906 | C2 | semidirect |
| 17. #13095519 | C8 | semidirect |
| 20. C2×#11715897 | C8 | semidirect |
| 25. C2×#11715895 | C8 | semidirect |
| 26. C8×D97 | C8 | semidirect |
| 27. C8×D97 | C8 | semidirect |
| 30. C2×C8×C97 | C8 | semidirect |
| 63. C97 | #1450 | semidirect |
| 90. C2×C8 | #11715906 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261848 | 2 |
| #20261819 | 2 |
| C8×#11715906 | 2 |
| C2×C8×#87604 | 2 |
| #1450 | 97 |