Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
476 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 476 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×#16811667 | C2 | semidirect |
| 2. C2×#16811538 | C2 | semidirect |
| 3. C2×#16811538 | C2 | semidirect |
| 4. #20290866 | C2 | semidirect |
| 5. #20289775 | C2 | semidirect |
| 6. (C2×#6157)⋊C16 | C2 | semidirect |
| 24. C2×#13133160 | C4 | semidirect |
| 25. C2×#13133160 | C4 | semidirect |
| 26. C2×D848 | C4 | semidirect |
| 28. C2×Q32×C53 | C4 | semidirect |
| 204. C2×Q32 | #6157 | semidirect |
| 220. C53 | #13011 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811667 | 2 |
| C2×#16811538 | 2 |
| #20290866 | 2 |
| #20289775 | 2 |
| (C2×#6157)⋊C16 | 2 |
| C2×#16811056 | 2 |
| #13011 | 53 |