Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
264 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 1. #20261848 | C2 | semidirect |
| 2. #20261821 | C2 | semidirect |
| 31. C22×Dic97 | C8 | semidirect |
| 36. C2×C4×D97 | C8 | semidirect |
| 37. C2×C4×D97 | C8 | semidirect |
| 40. C22×C4×C97 | C8 | semidirect |
| 105. C97 | #1458 | semidirect |
| 136. C22×C4 | #11715906 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261848 | 2 |
| #20261821 | 2 |
| #20261820 | 2 |
| C2×#15690889 | 2 |
| #1458 | 97 |