Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
378 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 86 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. #20291051 | C2 | semidirect |
| 4. #20290635 | C2 | semidirect |
| 5. #20289792 | C2 | semidirect |
| 6. #20289778 | C2 | semidirect |
| 22. #16810746 | C4 | semidirect |
| 23. #16810745 | C4 | semidirect |
| 24. #16810744 | C4 | semidirect |
| 30. C53×#444 | C4 | semidirect |
| 203. #444 | #6157 | semidirect |
| 219. C53 | #12830 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291051 | 2 |
| #20291035 | 2 |
| D53⋊#359 | 2 |
| #20290635 | 2 |
| #20289792 | 2 |
| #20289778 | 2 |
| #20283629 | 2 |
| #12830 | 53 |