Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
538 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 538 conjugacy classes of subgroups — too many to draw. Only its 86 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. C2×#16811664 | C2 | semidirect |
| 2. C2×#16811541 | C2 | semidirect |
| 3. C2×#16811540 | C2 | semidirect |
| 4. #20290869 | C2 | semidirect |
| 5. #20289780 | C2 | semidirect |
| 6. #20289755 | C2 | semidirect |
| 24. C2×#13133160 | C4 | semidirect |
| 25. C2×D848 | C4 | semidirect |
| 26. C2×#13133158 | C4 | semidirect |
| 28. C2×SD32×C53 | C4 | semidirect |
| 57. C2×D424 | C2×C4 | semidirect |
| 69. C2×#11719908 | C2×C4 | semidirect |
| 70. C2×Q16×C53 | C2×C4 | semidirect |
| 73. C2×C16×C53 | C2×C4 | semidirect |
| 219. C2×SD32 | #6157 | semidirect |
| 234. C53 | #13037 | semidirect |
| 242. C2×Q16 | C2×#6157 | semidirect |
| 270. C2×C16 | C2×#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811664 | 2 |
| C2×#16811541 | 2 |
| C2×#16811540 | 2 |
| #20290869 | 2 |
| #20289780 | 2 |
| #20289755 | 2 |
| C2×#16811060 | 2 |
| #13037 | 53 |