Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
146 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 46 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 |
|---|---|---|
| 1. #20261779 | C2 | semidirect |
| 2. #20261663 | C2 | semidirect |
| 3. #20261650 | C2 | semidirect |
| 4. C16×#87604 | C2 | semidirect |
| 12. #15690753 | C4 | semidirect |
| 13. D1552 | C4 | semidirect |
| 15. Q32×C97 | C4 | semidirect |
| 50. C97 | #2178 | semidirect |
| 58. Q32 | #87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261779 | 2 |
| #20261663 | 2 |
| #20261650 | 2 |
| C16×#87604 | 2 |
| #20261168 | 2 |
| #2178 | 97 |