Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
418 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 115 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. #20273463 | C2 | semidirect |
| 4. #20272573 | C2 | semidirect |
| 5. C53×#1835 | C2 | semidirect |
| 9. #16810702 | C4 | semidirect |
| 11. C8×D212 | C4 | semidirect |
| 131. #1835 | D53 | semidirect |
| 156. C53 | #8678 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283428 | 2 |
| #20273463 | 2 |
| #20273274 | 2 |
| #20272573 | 2 |
| C53×#1835 | 2 |
| #8678 | 53 |