Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
344 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 103 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. #20276514 | C2 | semidirect |
| 3. #20272774 | C2 | semidirect |
| 4. #20272760 | C2 | semidirect |
| 5. C53×#1564 | C2 | semidirect |
| 117. #1564 | D53 | semidirect |
| 140. C53 | #11948 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285294 | 2 |
| #20276514 | 2 |
| #20272774 | 2 |
| #20272760 | 2 |
| C53×#1564 | 2 |
| #11948 | 53 |