Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
658 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 658 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 |
|---|---|---|
| 2. #20284183 | C2 | semidirect |
| 3. #20279717 | C2 | semidirect |
| 4. #20273382 | C2 | semidirect |
| 5. #20273111 | C2 | semidirect |
| 6. #20272618 | C2 | semidirect |
| 7. C53×#1502 | C2 | semidirect |
| 113. C2×Dic106 | D8 | semidirect |
| 224. #1502 | D53 | semidirect |
| 257. C53 | #10242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285630 | 2 |
| #20284183 | 2 |
| #20279717 | 2 |
| #20273382 | 2 |
| #20273111 | 2 |
| #20272618 | 2 |
| C53×#1502 | 2 |
| #10242 | 53 |