Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
362 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 2. #20276497 | C2 | semidirect |
| 4. #20272817 | C2 | semidirect |
| 5. C53×#1384 | C2 | semidirect |
| 9. C2×#13133156 | C4 | semidirect |
| 11. C2×C16×D53 | C4 | semidirect |
| 102. #1384 | D53 | semidirect |
| 120. C53 | #12839 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811041 | 2 |
| #20276497 | 2 |
| #20274758 | 2 |
| #20272817 | 2 |
| C53×#1384 | 2 |
| #12839 | 53 |