Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
502 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 119 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. #20276297 | C2 | semidirect |
| 2. #20276268 | C2 | semidirect |
| 3. #20276173 | C2 | semidirect |
| 4. #20276112 | C2 | semidirect |
| 5. #20275988 | C2 | semidirect |
| 6. #20275972 | C2 | semidirect |
| 8. #20275195 | C2 | semidirect |
| 9. C53×#1858 | C2 | semidirect |
| 149. #1858 | D53 | semidirect |
| 176. C53 | #32870 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276297 | 2 |
| #20276268 | 2 |
| #20276173 | 2 |
| #20276112 | 2 |
| #20275988 | 2 |
| #20275972 | 2 |
| #20275824 | 2 |
| #20275195 | 2 |
| C53×#1858 | 2 |
| #32870 | 53 |