Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
548 conjugacy classes of subgroups; only the 238 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 238 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. Q8×#11719910 | C2 | semidirect |
| 2. #20291101 | C2 | semidirect |
| 3. #20291079 | C2 | semidirect |
| 4. C4×#13133292 | C2 | semidirect |
| 58. #11719910 | #41 | semidirect |
| 60. Q8×C53 | M32 | semidirect |
| 110. C53 | #33485 | semidirect |
| 152. Q8 | #13133292 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11719910 | 2 |
| #20291101 | 2 |
| #20291079 | 2 |
| C4×#13133292 | 2 |
| C8×#11719949 | 2 |
| #33485 | 53 |