Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
464 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 77 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. #20275146 | C2 | semidirect |
| 4. #20274919 | C2 | semidirect |
| 6. #20273080 | C2 | semidirect |
| 7. C53×#1305 | C2 | semidirect |
| 213. #1305 | D53 | semidirect |
| 243. C53 | #10562 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285522 | 2 |
| #20275176 | 2 |
| #20275146 | 2 |
| #20274919 | 2 |
| #20273282 | 2 |
| #20273080 | 2 |
| C53×#1305 | 2 |
| #10562 | 53 |