Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
416 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 82 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. #20291063 | C2 | semidirect |
| 4. #20290834 | C2 | semidirect |
| 5. #20289795 | C2 | semidirect |
| 6. #20289767 | C2 | semidirect |
| 25. #16810437 | C4 | semidirect |
| 26. #16810436 | C4 | semidirect |
| 27. #16810435 | C4 | semidirect |
| 28. C53×#361 | C4 | semidirect |
| 61. #13133157 | C2×C4 | semidirect |
| 64. #13133153 | C2×C4 | semidirect |
| 67. M32×C53 | C2×C4 | semidirect |
| 68. #108×C53 | C2×C4 | semidirect |
| 197. #361 | #6157 | semidirect |
| 199. C53 | #12953 | semidirect |
| 223. M32 | C2×#6157 | semidirect |
| 232. #108 | C2×#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291474 | 2 |
| #20291063 | 2 |
| C2×#16811541 | 2 |
| #20290834 | 2 |
| #20289795 | 2 |
| #20289767 | 2 |
| #361×D53 | 2 |
| #12953 | 53 |