Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
332 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 2. C2×C16×Dic53 | C2 | semidirect |
| 4. #20275464 | C2 | semidirect |
| 5. #20272810 | C2 | semidirect |
| 6. #20272809 | C2 | semidirect |
| 21. C53×#358 | C4 | semidirect |
| 22. C53×#357 | C4 | semidirect |
| 156. #358 | Dic53 | semidirect |
| 157. #357 | Dic53 | semidirect |
| 160. C53 | #13151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810430 | 2 |
| C2×C16×Dic53 | 2 |
| #20275604 | 2 |
| #20275464 | 2 |
| #20272810 | 2 |
| #20272809 | 2 |
| C53×#2138 | 2 |
| #13151 | 53 |