Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
368 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 81 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. #20276511 | C2 | semidirect |
| 3. #20274616 | C2 | semidirect |
| 4. #20272731 | C2 | semidirect |
| 5. #20272730 | C2 | semidirect |
| 6. #20272729 | C2 | semidirect |
| 7. C53×#1349 | C2 | semidirect |
| 160. #1349 | D53 | semidirect |
| 186. C53 | #11747 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285289 | 2 |
| #20276511 | 2 |
| #20274616 | 2 |
| #20272731 | 2 |
| #20272730 | 2 |
| #20272729 | 2 |
| C53×#1349 | 2 |
| #11747 | 53 |