Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
490 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 490 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 |
|---|---|---|
| 2. C2×#16811549 | C2 | semidirect |
| 4. #20290819 | C2 | semidirect |
| 5. #20289772 | C2 | semidirect |
| 6. (C2×#6157)⋊C16 | C2 | semidirect |
| 23. #16810425 | C4 | semidirect |
| 24. #16810424 | C4 | semidirect |
| 25. #16810423 | C4 | semidirect |
| 26. C53×#357 | C4 | semidirect |
| 56. C2×#11719908 | C2×C4 | semidirect |
| 59. #13133151 | C2×C4 | semidirect |
| 62. C2×C16×C53 | C2×C4 | semidirect |
| 63. #107×C53 | C2×C4 | semidirect |
| 93. D8×C53 | C4⋊C4 | semidirect |
| 102. D424 | C4⋊C4 | semidirect |
| 214. #357 | #6157 | semidirect |
| 216. C53 | #12935 | semidirect |
| 242. C2×C16 | C2×#6157 | semidirect |
| 249. #107 | C2×#6157 | semidirect |
| 276. D8 | C4⋊#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×#16811549 | 2 |
| C2×#16811535 | 2 |
| #20290819 | 2 |
| #20289772 | 2 |
| (C2×#6157)⋊C16 | 2 |
| #357×D53 | 2 |
| #12935 | 53 |