Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
478 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 99 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. #20283800 | C2 | semidirect |
| 4. #20272580 | C2 | semidirect |
| 5. C4×#101×C53 | C2 | semidirect |
| 169. C4×#101 | D53 | semidirect |
| 197. C53 | #9188 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283800 | 2 |
| #20280575 | 2 |
| #20273312 | 2 |
| #20272580 | 2 |
| C4×#101×C53 | 2 |
| #9188 | 53 |