Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
812 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 812 conjugacy classes of subgroups — too many to draw. Only its 103 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. #20283160 | C2 | semidirect |
| 3. #20273041 | C2 | semidirect |
| 4. #20272624 | C2 | semidirect |
| 5. C53×#1785 | C2 | semidirect |
| 48. C22⋊#88322 | D4 | semidirect |
| 244. #1785 | D53 | semidirect |
| 275. C53 | #9511 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283160 | 2 |
| #20278030 | 2 |
| #20273041 | 2 |
| #20272624 | 2 |
| C53×#1785 | 2 |
| #9511 | 53 |