Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
476 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 82 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. #20291478 | C2 | semidirect |
| 2. #20291035 | C2 | semidirect |
| 3. C2×#16811540 | C2 | semidirect |
| 4. #20290874 | C2 | semidirect |
| 5. #20289787 | C2 | semidirect |
| 6. #20289767 | C2 | semidirect |
| 25. #16811064 | C4 | semidirect |
| 26. #16811061 | C4 | semidirect |
| 28. #16811058 | C4 | semidirect |
| 32. C53×#510 | C4 | semidirect |
| 69. C2×D424 | C2×C4 | semidirect |
| 78. #13133157 | C2×C4 | semidirect |
| 82. C2×Q16×C53 | C2×C4 | semidirect |
| 85. M32×C53 | C2×C4 | semidirect |
| 229. #510 | #6157 | semidirect |
| 249. C53 | #13030 | semidirect |
| 263. C2×Q16 | C2×#6157 | semidirect |
| 290. M32 | C2×#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291478 | 2 |
| #20291035 | 2 |
| C2×#16811540 | 2 |
| #20290874 | 2 |
| #20289787 | 2 |
| #20289767 | 2 |
| #20287850 | 2 |
| #13030 | 53 |