Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
284 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 11. #15690810 | C4 | semidirect |
| 12. #15690801 | C4 | semidirect |
| 19. C4⋊Q8×C97 | C4 | semidirect |
| 26. C4×#87604 | Q8 | semidirect |
| 82. C97 | #1994 | semidirect |
| 89. C4⋊Q8 | #87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261739 | 2 |
| C42×#87604 | 2 |
| #20261605 | 2 |
| #20261290 | 2 |
| #1994 | 97 |