Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
554 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 111 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. #20272597 | C2 | semidirect |
| 4. #20272596 | C2 | semidirect |
| 5. C53×#1295 | C2 | semidirect |
| 130. #1295 | D53 | semidirect |
| 148. C53 | #8719 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #382×D53 | 2 |
| #20274478 | 2 |
| #20272597 | 2 |
| #20272596 | 2 |
| C53×#1295 | 2 |
| #8719 | 53 |