Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
456 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 88 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. #20290099 | C2 | semidirect |
| 4. #20290065 | C2 | semidirect |
| 5. #20289607 | C2 | semidirect |
| 6. #20289549 | C2 | semidirect |
| 26. #16810910 | C4 | semidirect |
| 27. #16810908 | C4 | semidirect |
| 28. #16810904 | C4 | semidirect |
| 32. C53×#477 | C4 | semidirect |
| 220. #477 | #6157 | semidirect |
| 241. C53 | #9209 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291523 | 2 |
| #20290588 | 2 |
| #20290099 | 2 |
| #20290065 | 2 |
| #20289607 | 2 |
| #20289549 | 2 |
| #20284506 | 2 |
| #9209 | 53 |