Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
288 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 55 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. #20287853 | C2 | semidirect |
| 2. #20277027 | C2 | semidirect |
| 3. C2×D1696 | C2 | semidirect |
| 4. #20276836 | C2 | semidirect |
| 5. #20272904 | C2 | semidirect |
| 6. #20272856 | C2 | semidirect |
| 7. C53×#1417 | C2 | semidirect |
| 13. C2×D848 | C22 | semidirect |
| 20. #16810457 | C22 | semidirect |
| 23. C2×C32×C53 | C22 | semidirect |
| 24. C53×#368 | C22 | semidirect |
| 121. #1417 | D53 | semidirect |
| 143. C2×C32 | C2×D53 | semidirect |
| 144. #368 | C2×D53 | semidirect |
| 146. C53 | #13669 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287853 | 2 |
| #20277027 | 2 |
| C2×D1696 | 2 |
| #20276836 | 2 |
| #20272904 | 2 |
| #20272856 | 2 |
| C53×#1417 | 2 |
| #13669 | 53 |