Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
500 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 91 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. C4×#13133132 | C2 | semidirect |
| 2. #20273033 | C2 | semidirect |
| 3. #20272736 | C2 | semidirect |
| 4. #20272712 | C2 | semidirect |
| 12. C2×#124×C53 | C4 | semidirect |
| 15. C53×#393 | C4 | semidirect |
| 18. C53×#392 | C4 | semidirect |
| 22. C53×#383 | C4 | semidirect |
| 203. C2×#124 | Dic53 | semidirect |
| 208. #393 | Dic53 | semidirect |
| 211. #392 | Dic53 | semidirect |
| 215. #383 | Dic53 | semidirect |
| 220. C53 | #11730 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13133132 | 2 |
| #20273033 | 2 |
| #20272736 | 2 |
| #20272712 | 2 |
| C53×#2631 | 2 |
| #11730 | 53 |