Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
370 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 97 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. C2×#16811025 | C2 | semidirect |
| 4. #20272814 | C2 | semidirect |
| 5. C53×#1376 | C2 | semidirect |
| 114. #1376 | D53 | semidirect |
| 131. C53 | #13372 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811025 | 2 |
| C2×#16810434 | 2 |
| #20275603 | 2 |
| #20272814 | 2 |
| C53×#1376 | 2 |
| #13372 | 53 |