Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
356 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 89 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. #20274855 | C2 | semidirect |
| 3. #20273489 | C2 | semidirect |
| 6. #20272545 | C2 | semidirect |
| 7. C53×#1570 | C2 | semidirect |
| 132. #1570 | D53 | semidirect |
| 154. C53 | #10659 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20275512 | 2 |
| #20274855 | 2 |
| #20273489 | 2 |
| #20273141 | 2 |
| #20273139 | 2 |
| #20272545 | 2 |
| C53×#1570 | 2 |
| #10659 | 53 |