Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
286 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 286 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. #20260595 | C2 | semidirect |
| 3. #20260473 | C2 | semidirect |
| 4. #20260470 | C2 | semidirect |
| 5. #407×C97 | C2 | semidirect |
| 6. C2×#13095511 | C4 | semidirect |
| 8. #15690789 | C4 | semidirect |
| 10. #15690784 | C4 | semidirect |
| 15. #15690769 | C4 | semidirect |
| 118. C97 | #1513 | semidirect |
| 120. #407 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261246 | 2 |
| #20260595 | 2 |
| #20260473 | 2 |
| #20260470 | 2 |
| #407×C97 | 2 |
| #1513 | 97 |