Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
246 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 77 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. #20260788 | C2 | semidirect |
| 3. #20260465 | C2 | semidirect |
| 4. #20260462 | C2 | semidirect |
| 5. #432×C97 | C2 | semidirect |
| 98. C97 | #1488 | semidirect |
| 100. #432 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13095511 | 2 |
| #20260788 | 2 |
| #20260465 | 2 |
| #20260462 | 2 |
| #432×C97 | 2 |
| #1488 | 97 |