Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
434 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 434 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 |
|---|---|---|
| 2. C2×#16810438 | C2 | semidirect |
| 5. #20276434 | C2 | semidirect |
| 6. #20276320 | C2 | semidirect |
| 7. C53×#1833 | C2 | semidirect |
| 15. #16811007 | C4 | semidirect |
| 16. #16811003 | C4 | semidirect |
| 170. #1833 | D53 | semidirect |
| 195. C53 | #13216 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285209 | 2 |
| C2×#16810438 | 2 |
| #20276450 | 2 |
| #20276442 | 2 |
| #20276434 | 2 |
| #20276320 | 2 |
| C53×#1833 | 2 |
| #13216 | 53 |