Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
224 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 83 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. Q16×#88322 | C2 | semidirect |
| 3. #20272787 | C2 | semidirect |
| 4. #20272679 | C2 | semidirect |
| 6. #20272634 | C2 | semidirect |
| 48. Q16×C53 | M16 | semidirect |
| 128. C53 | #12075 | semidirect |
| 154. Q16 | #11719917 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20273600 | 2 |
| Q16×#88322 | 2 |
| #20272787 | 2 |
| #20272679 | 2 |
| #20272676 | 2 |
| #20272634 | 2 |
| C4×SD32×C53 | 2 |
| #12075 | 53 |