Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
180 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 73 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. #20261825 | C2 | semidirect |
| 3. #20261824 | C2 | semidirect |
| 27. C2×#11715895 | C8 | semidirect |
| 28. C8×D97 | C8 | semidirect |
| 29. C8×D97 | C8 | semidirect |
| 32. C2×C8×C97 | C8 | semidirect |
| 72. C97 | #1564 | semidirect |
| 100. 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 |
| #20261825 | 2 |
| #20261824 | 2 |
| C2×C8×#87604 | 2 |
| #1564 | 97 |