Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
216 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 79 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. #20276553 | C2 | semidirect |
| 3. #20272791 | C2 | semidirect |
| 4. #20272689 | C2 | semidirect |
| 5. C8×C16×C53 | C2 | semidirect |
| 18. Dic424 | C8 | semidirect |
| 19. #13133162 | C8 | semidirect |
| 20. D848 | C8 | semidirect |
| 73. C8×C16 | D53 | semidirect |
| 87. C53 | #12046 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276597 | 2 |
| #20276553 | 2 |
| #20272791 | 2 |
| #20272689 | 2 |
| C8×C16×C53 | 2 |
| #12046 | 53 |