Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
636 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 636 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 1. #20285160 | C2 | semidirect |
| 2. #20284715 | C2 | semidirect |
| 3. #20275514 | C2 | semidirect |
| 4. #20273115 | C2 | semidirect |
| 5. #20273114 | C2 | semidirect |
| 6. #20272545 | C2 | semidirect |
| 7. C53×#3100 | C2 | semidirect |
| 141. C2×#88322 | D8 | semidirect |
| 217. #3100 | D53 | semidirect |
| 254. C53 | #10032 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285160 | 2 |
| #20284715 | 2 |
| #20275514 | 2 |
| #20273115 | 2 |
| #20273114 | 2 |
| #20272545 | 2 |
| C53×#3100 | 2 |
| #10032 | 53 |