Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
554 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 554 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×#16811536 | C2 | semidirect |
| 4. #20290861 | C2 | semidirect |
| 5. #20289773 | C2 | semidirect |
| 6. (C2×#6157)⋊C16 | C2 | semidirect |
| 22. C2×#13133162 | C4 | semidirect |
| 23. C2×#13133161 | C4 | semidirect |
| 24. C2×#13133160 | C4 | semidirect |
| 28. C2×SD32×C53 | C4 | semidirect |
| 52. C2×Dic212 | C2×C4 | semidirect |
| 68. C2×#11719908 | C2×C4 | semidirect |
| 71. C2×Q16×C53 | C2×C4 | semidirect |
| 74. C2×C16×C53 | C2×C4 | semidirect |
| 151. C2×#6157 | SD32 | semidirect |
| 231. C2×SD32 | #6157 | semidirect |
| 244. C53 | #13014 | semidirect |
| 254. C2×Q16 | C2×#6157 | semidirect |
| 280. 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×D8×#6157 | 2 |
| C2×#16811536 | 2 |
| C2×#16811535 | 2 |
| #20290861 | 2 |
| #20289773 | 2 |
| (C2×#6157)⋊C16 | 2 |
| C2×SD32×D53 | 2 |
| #13014 | 53 |