Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
304 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 4. #20272773 | C2 | semidirect |
| 5. Q8⋊#11719908 | C2 | semidirect |
| 6. #20272679 | C2 | semidirect |
| 7. Q8×Q16×C53 | C2 | semidirect |
| 61. Q16×C53 | SD16 | semidirect |
| 90. Q8×C53 | SD32 | semidirect |
| 124. Q8×Q16 | D53 | semidirect |
| 152. C53 | #12354 | semidirect |
| 189. Q16 | #11719924 | semidirect |
| 218. Q8 | #13133160 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276940 | 2 |
| #20276755 | 2 |
| #20274075 | 2 |
| #20272773 | 2 |
| Q8⋊#11719908 | 2 |
| #20272679 | 2 |
| Q8×Q16×C53 | 2 |
| #12354 | 53 |