Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
224 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 3. #20272778 | C2 | semidirect |
| 4. Q8⋊#11719908 | C2 | semidirect |
| 6. C16×#88322 | C2 | semidirect |
| 7. C53×#2183 | C2 | semidirect |
| 65. C16×C53 | SD16 | semidirect |
| 88. #88322 | M32 | semidirect |
| 102. #2183 | D53 | semidirect |
| 128. C53 | #12051 | semidirect |
| 173. C16 | #11719924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276548 | 2 |
| C8×#11719924 | 2 |
| #20272778 | 2 |
| Q8⋊#11719908 | 2 |
| #20272669 | 2 |
| C16×#88322 | 2 |
| C53×#2183 | 2 |
| #12051 | 53 |