Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
298 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 298 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. #20276944 | C2 | semidirect |
| 3. #20276766 | C2 | semidirect |
| 5. #20272678 | C2 | semidirect |
| 7. C53×#1365 | C2 | semidirect |
| 96. D212 | Q32 | semidirect |
| 128. #1365 | D53 | semidirect |
| 152. C53 | #12346 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287107 | 2 |
| #20276944 | 2 |
| #20276766 | 2 |
| #20274081 | 2 |
| #20272678 | 2 |
| #20272669 | 2 |
| C53×#1365 | 2 |
| #12346 | 53 |