Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
218 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 53 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. #20261114 | C2 | semidirect |
| 3. #20261026 | C2 | semidirect |
| 4. #20260462 | C2 | semidirect |
| 5. #333×C97 | C2 | semidirect |
| 61. C97 | #1634 | semidirect |
| 65. #333 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261451 | 2 |
| #20261114 | 2 |
| #20261026 | 2 |
| #20260462 | 2 |
| #333×C97 | 2 |
| #1634 | 97 |