Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1022 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 1022 conjugacy classes of subgroups — too many to draw. Only its 191 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. #20288525 | C2 | semidirect |
| 4. #20275872 | C2 | semidirect |
| 5. #20275659 | C2 | semidirect |
| 6. #20275116 | C2 | semidirect |
| 7. C4×#101×C53 | C2 | semidirect |
| 182. C4×#101 | D53 | semidirect |
| 212. C53 | #25920 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20288525 | 2 |
| #20285090 | 2 |
| #20279714 | 2 |
| #20275872 | 2 |
| #20275659 | 2 |
| #20275116 | 2 |
| C4×#101×C53 | 2 |
| #25920 | 53 |