Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
590 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 590 conjugacy classes of subgroups — too many to draw. Only its 96 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×D8×#6157 | C2 | semidirect |
| 2. C2×#16811535 | C2 | semidirect |
| 3. C2×#16811535 | C2 | semidirect |
| 4. #20290862 | C2 | semidirect |
| 5. #20289773 | C2 | semidirect |
| 6. (C2×#6157)⋊C16 | C2 | semidirect |
| 22. C2×D848 | C4 | semidirect |
| 23. C2×#13133158 | C4 | semidirect |
| 24. C2×#13133158 | C4 | semidirect |
| 28. C2×D16×C53 | C4 | semidirect |
| 53. C2×D424 | C2×C4 | semidirect |
| 68. C2×#11719908 | C2×C4 | semidirect |
| 72. C2×D8×C53 | C2×C4 | semidirect |
| 74. C2×C16×C53 | C2×C4 | semidirect |
| 114. D8×C53 | C22⋊C4 | semidirect |
| 124. D424 | C22⋊C4 | semidirect |
| 161. C2×#6157 | D16 | semidirect |
| 247. C2×D16 | #6157 | semidirect |
| 260. C53 | #13012 | semidirect |
| 277. C2×D8 | C2×#6157 | semidirect |
| 298. C2×C16 | C2×#6157 | semidirect |
| 342. D8 | C22⋊#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×#6157 | 2 |
| C2×#16811535 | 2 |
| #20290862 | 2 |
| #20289773 | 2 |
| (C2×#6157)⋊C16 | 2 |
| C2×D16×D53 | 2 |
| #13012 | 53 |