Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
142 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 44 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. #20261775 | C2 | semidirect |
| 3. #20261660 | C2 | semidirect |
| 4. #20261654 | C2 | semidirect |
| 6. #20261625 | C2 | semidirect |
| 18. Dic776 | C4 | semidirect |
| 19. #15690756 | C4 | semidirect |
| 20. #15690754 | C4 | semidirect |
| 22. SD32×C97 | C4 | semidirect |
| 71. C97 | #2180 | semidirect |
| 86. SD32 | #87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261782 | 2 |
| #20261775 | 2 |
| #20261660 | 2 |
| #20261654 | 2 |
| #20261651 | 2 |
| #20261625 | 2 |
| #20261174 | 2 |
| #2180 | 97 |