Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
668 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 81 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. #20281740 | C2 | semidirect |
| 2. #20275803 | C2 | semidirect |
| 3. #20275786 | C2 | semidirect |
| 4. #20272540 | C2 | semidirect |
| 5. #20272536 | C2 | semidirect |
| 6. #20272535 | C2 | semidirect |
| 7. C53×#2011 | C2 | semidirect |
| 114. C2×Dic106 | D8 | semidirect |
| 255. #2011 | D53 | semidirect |
| 288. C53 | #7742 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20281740 | 2 |
| #20275803 | 2 |
| #20275786 | 2 |
| #20272540 | 2 |
| #20272536 | 2 |
| #20272535 | 2 |
| C53×#2011 | 2 |
| #7742 | 53 |