Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
184 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 76 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. #20291139 | C2 | semidirect |
| 2. #20291138 | C2 | semidirect |
| 3. #20289875 | C2 | semidirect |
| 4. #20289833 | C2 | semidirect |
| 5. #20289832 | C2 | semidirect |
| 6. #20289823 | C2 | semidirect |
| 114. C53 | #13648 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291139 | 2 |
| #20291138 | 2 |
| #20289875 | 2 |
| #20289833 | 2 |
| #20289832 | 2 |
| #20289823 | 2 |
| #20276549 | 2 |
| #13648 | 53 |