Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
508 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 101 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. #20272594 | C2 | semidirect |
| 5. #20272582 | C2 | semidirect |
| 6. #20272563 | C2 | semidirect |
| 7. C53×#2549 | C2 | semidirect |
| 27. C22×D212 | Q8 | semidirect |
| 36. C2×C4⋊Dic53 | Q8 | semidirect |
| 220. #2549 | D53 | semidirect |
| 256. C53 | #10374 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20275551 | 2 |
| #20273282 | 2 |
| C2×#16810356 | 2 |
| #20272594 | 2 |
| #20272582 | 2 |
| #20272563 | 2 |
| C53×#2549 | 2 |
| #10374 | 53 |