Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
462 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 103 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. #20277521 | C2 | semidirect |
| 3. #20273317 | C2 | semidirect |
| 5. #20272581 | C2 | semidirect |
| 6. #20272570 | C2 | semidirect |
| 25. C53×#501 | C4 | semidirect |
| 26. C53×#490 | C4 | semidirect |
| 207. #501 | Dic53 | semidirect |
| 208. #490 | Dic53 | semidirect |
| 228. C53 | #9382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20277521 | 2 |
| #20275635 | 2 |
| #20273317 | 2 |
| #20273262 | 2 |
| #20272581 | 2 |
| #20272570 | 2 |
| C53×#3234 | 2 |
| #9382 | 53 |