Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
414 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 74 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. #20290903 | C2 | semidirect |
| 4. #20290078 | C2 | semidirect |
| 5. #20289604 | C2 | semidirect |
| 6. #20289600 | C2 | semidirect |
| 26. #16811017 | C4 | semidirect |
| 27. #16810993 | C4 | semidirect |
| 28. #16810985 | C4 | semidirect |
| 34. C53×#501 | C4 | semidirect |
| 208. #501 | #6157 | semidirect |
| 233. C53 | #8998 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291673 | 2 |
| #20290903 | 2 |
| #20290089 | 2 |
| #20290078 | 2 |
| #20289604 | 2 |
| #20289600 | 2 |
| #20285323 | 2 |
| #8998 | 53 |