Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
556 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 131 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. #20276290 | C2 | semidirect |
| 2. #20275890 | C2 | semidirect |
| 3. #20275886 | C2 | semidirect |
| 4. #20275690 | C2 | semidirect |
| 7. #20274958 | C2 | semidirect |
| 8. #20274952 | C2 | semidirect |
| 9. C53×#2102 | C2 | semidirect |
| 36. #13133217 | Q8 | semidirect |
| 38. #13133214 | Q8 | semidirect |
| 40. #13133205 | Q8 | semidirect |
| 153. #2102 | D53 | semidirect |
| 186. C53 | #32704 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276290 | 2 |
| #20275890 | 2 |
| #20275886 | 2 |
| #20275690 | 2 |
| #20275542 | 2 |
| #20275097 | 2 |
| #20274958 | 2 |
| #20274952 | 2 |
| C53×#2102 | 2 |
| #32704 | 53 |