Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
230 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
|---|---|---|
| 19. #15690744 | C4 | semidirect |
| 20. #15690743 | C4 | semidirect |
| 21. #15690743 | C4 | semidirect |
| 22. #107×C97 | C4 | semidirect |
| 108. C97 | #1918 | semidirect |
| 128. #107 | #87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261686 | 2 |
| C4⋊C4×#87604 | 2 |
| #20261609 | 2 |
| #20261608 | 2 |
| #20261600 | 2 |
| #107×D97 | 2 |
| #1918 | 97 |