Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
536 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 536 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 |
|---|---|---|
| 4. #20272541 | C2 | semidirect |
| 5. #20272541 | C2 | semidirect |
| 6. #20272538 | C2 | semidirect |
| 7. C53×#2806 | C2 | semidirect |
| 73. C2×Q8×C53 | SD16 | semidirect |
| 111. C4⋊C4×C53 | SD16 | semidirect |
| 209. #2806 | D53 | semidirect |
| 243. C53 | #7748 | semidirect |
| 290. C2×Q8 | #11719924 | semidirect |
| 339. C4⋊C4 | #11719924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20275949 | 2 |
| #20275802 | 2 |
| #20272541 | 2 |
| #20272538 | 2 |
| C53×#2806 | 2 |
| #7748 | 53 |