Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
456 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 160 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. Q16×#87604 | C2 | semidirect |
| 20. C2×Dic388 | C4 | semidirect |
| 21. C2×#13095501 | C4 | semidirect |
| 22. Q16×D97 | C4 | semidirect |
| 23. Q16×D97 | C4 | semidirect |
| 27. C2×Q16×C97 | C4 | semidirect |
| 101. C97 | #2950 | semidirect |
| 116. C2×Q16 | #87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261803 | 2 |
| #20261775 | 2 |
| Q16×#87604 | 2 |
| #20261745 | 2 |
| #20261728 | 2 |
| #20261698 | 2 |
| C2×Q16×D97 | 2 |
| #2950 | 97 |