Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
380 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 90 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. D53⋊#365 | C2 | semidirect |
| 3. C2×#16811548 | C2 | semidirect |
| 5. #20289793 | C2 | semidirect |
| 6. #20289785 | C2 | semidirect |
| 25. #16810408 | C4 | semidirect |
| 26. #16810407 | C4 | semidirect |
| 27. #16810406 | C4 | semidirect |
| 28. C53×#350 | C4 | semidirect |
| 202. #350 | #6157 | semidirect |
| 204. C53 | #12933 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291376 | 2 |
| D53⋊#365 | 2 |
| C2×#16811548 | 2 |
| #20290603 | 2 |
| #20289793 | 2 |
| #20289785 | 2 |
| #20276341 | 2 |
| #12933 | 53 |