Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
244 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 67 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. #20276623 | C2 | semidirect |
| 3. #20274076 | C2 | semidirect |
| 4. #20272760 | C2 | semidirect |
| 5. C53×#1372 | C2 | semidirect |
| 50. C16×C53 | SD16 | semidirect |
| 83. #1372 | D53 | semidirect |
| 100. C53 | #12442 | semidirect |
| 135. C16 | #11719913 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276965 | 2 |
| #20276623 | 2 |
| #20274076 | 2 |
| #20272760 | 2 |
| C53×#1372 | 2 |
| #12442 | 53 |