Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
246 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 246 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. #20260792 | C2 | semidirect |
| 3. #20260480 | C2 | semidirect |
| 4. #20260478 | C2 | semidirect |
| 5. #423×C97 | C2 | semidirect |
| 85. C97 | #1557 | semidirect |
| 88. #423 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261285 | 2 |
| #20260792 | 2 |
| #20260480 | 2 |
| #20260478 | 2 |
| #423×C97 | 2 |
| #1557 | 97 |