Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
486 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 4. #20275587 | C2 | semidirect |
| 5. #20272820 | C2 | semidirect |
| 6. #20272798 | C2 | semidirect |
| 7. C53×#2141 | C2 | semidirect |
| 11. #16811064 | C4 | semidirect |
| 47. #13133157 | C2×C4 | semidirect |
| 63. C2×Q16×C53 | C2×C4 | semidirect |
| 175. #2141 | D53 | semidirect |
| 204. C53 | #13026 | semidirect |
| 217. C2×Q16 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811064 | 2 |
| #20283515 | 2 |
| C2×#16810434 | 2 |
| #20275587 | 2 |
| #20272820 | 2 |
| #20272798 | 2 |
| C53×#2141 | 2 |
| #13026 | 53 |