Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
514 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 155 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. #20276990 | C2 | semidirect |
| 3. #20276942 | C2 | semidirect |
| 5. Q32×Dic53 | C2 | semidirect |
| 7. C53×#2247 | C2 | semidirect |
| 90. C4×D53 | Q32 | semidirect |
| 112. #2247 | D53 | semidirect |
| 137. C53 | #33734 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285299 | 2 |
| #20276990 | 2 |
| #20276942 | 2 |
| #20276803 | 2 |
| Q32×Dic53 | 2 |
| C4×C16×D53 | 2 |
| C53×#2247 | 2 |
| #33734 | 53 |