Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
252 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 79 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. #20260784 | C2 | semidirect |
| 3. #20260783 | C2 | semidirect |
| 6. #20260500 | C2 | semidirect |
| 7. #341×C97 | C2 | semidirect |
| 92. C97 | #1858 | semidirect |
| 99. #341 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261501 | 2 |
| #20260784 | 2 |
| #20260783 | 2 |
| #20260717 | 2 |
| #20260701 | 2 |
| #20260500 | 2 |
| #341×C97 | 2 |
| #1858 | 97 |