Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
772 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 772 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 |
|---|---|---|
| 1. #20283763 | C2 | semidirect |
| 2. #20274646 | C2 | semidirect |
| 3. #20274636 | C2 | semidirect |
| 4. #20273258 | C2 | semidirect |
| 5. #20272622 | C2 | semidirect |
| 6. #20272591 | C2 | semidirect |
| 28. C53×#450 | C4 | semidirect |
| 30. C53×#447 | C4 | semidirect |
| 286. #450 | Dic53 | semidirect |
| 288. #447 | Dic53 | semidirect |
| 307. C53 | #9520 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283763 | 2 |
| #20274646 | 2 |
| #20274636 | 2 |
| #20273258 | 2 |
| #20272622 | 2 |
| #20272591 | 2 |
| C53×#3003 | 2 |
| #9520 | 53 |