Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
440 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 99 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. #20275692 | C2 | semidirect |
| 4. #20273403 | C2 | semidirect |
| 6. #20272590 | C2 | semidirect |
| 7. C53×#1842 | C2 | semidirect |
| 96. C42×C53 | SD16 | semidirect |
| 188. #1842 | D53 | semidirect |
| 219. C53 | #10520 | semidirect |
| 306. C42 | #11719913 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20286032 | 2 |
| #20275692 | 2 |
| #20275543 | 2 |
| #20273403 | 2 |
| #20273390 | 2 |
| #20272590 | 2 |
| C53×#1842 | 2 |
| #10520 | 53 |