Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
420 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 95 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. #20275691 | C2 | semidirect |
| 4. #20274831 | C2 | semidirect |
| 5. #20273406 | C2 | semidirect |
| 7. C53×#1292 | C2 | semidirect |
| 115. C4×Dic53 | SD16 | semidirect |
| 190. #1292 | D53 | semidirect |
| 218. C53 | #10521 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20286032 | 2 |
| #20275691 | 2 |
| #20275542 | 2 |
| #20274831 | 2 |
| #20273406 | 2 |
| #20273393 | 2 |
| C53×#1292 | 2 |
| #10521 | 53 |