Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
536 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 87 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. #20281746 | C2 | semidirect |
| 5. #20272540 | C2 | semidirect |
| 6. #20272539 | C2 | semidirect |
| 7. C53×#1271 | C2 | semidirect |
| 110. C4⋊C4×C53 | SD16 | semidirect |
| 116. C4⋊Dic53 | SD16 | semidirect |
| 215. #1271 | D53 | semidirect |
| 243. C53 | #7741 | semidirect |
| 340. C4⋊C4 | #11719913 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20281746 | 2 |
| #20275950 | 2 |
| #20275949 | 2 |
| #20275805 | 2 |
| #20272540 | 2 |
| #20272539 | 2 |
| C53×#1271 | 2 |
| #7741 | 53 |