Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
332 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 3. C2×C16×Dic53 | C2 | semidirect |
| 5. #20275464 | C2 | semidirect |
| 6. #20272808 | C2 | semidirect |
| 7. C53×#1382 | C2 | semidirect |
| 16. #16810426 | C4 | semidirect |
| 17. #16810423 | C4 | semidirect |
| 138. #1382 | D53 | 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×#16810431 | 2 |
| #20276420 | 2 |
| C2×C16×Dic53 | 2 |
| #20275601 | 2 |
| #20275464 | 2 |
| #20272808 | 2 |
| C53×#1382 | 2 |
| #13151 | 53 |