Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
954 conjugacy classes of subgroups; only the 264 normal subgroups are shown.
This group has 954 conjugacy classes of subgroups — too many to draw. Only its 264 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 |
|---|---|---|
| 7. #16811559 | C4 | semidirect |
| 8. C42×#6157 | C4 | semidirect |
| 9. #16811491 | C4 | semidirect |
| 13. C2×#13133128 | C4 | semidirect |
| 14. C2×C8×Dic53 | C4 | semidirect |
| 15. C2×#97×C53 | C4 | semidirect |
| 56. C4×#6157 | C42 | semidirect |
| 59. C2×C8×C53 | C42 | semidirect |
| 69. C2×#88322 | C42 | semidirect |
| 108. Dic53 | H(3,ℤ/4) | semidirect |
| 122. C2×#97 | #6157 | semidirect |
| 129. C53 | C4×H(3,ℤ/4) | semidirect |
| 172. C2×C8 | C4×#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13133296 | 2 |
| C2×#16811491 | 2 |
| C2×#16810575 | 2 |
| C4×H(3,ℤ/4) | 53 |