Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
554 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 83 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. #20275949 | C2 | semidirect |
| 2. #20275802 | C2 | semidirect |
| 4. #20272541 | C2 | semidirect |
| 5. #20272538 | C2 | semidirect |
| 6. #20272536 | C2 | semidirect |
| 7. C53×#2808 | C2 | semidirect |
| 223. #2808 | D53 | semidirect |
| 258. C53 | #7746 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20275949 | 2 |
| #20275802 | 2 |
| #20275785 | 2 |
| #20272541 | 2 |
| #20272538 | 2 |
| #20272536 | 2 |
| C53×#2808 | 2 |
| #7746 | 53 |