Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
234 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 71 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. #20274333 | C2 | semidirect |
| 4. #20272769 | C2 | semidirect |
| 5. C53×#1370 | C2 | semidirect |
| 51. D424 | Q16 | semidirect |
| 88. #1370 | D53 | semidirect |
| 105. C53 | #12445 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276853 | 2 |
| #20274333 | 2 |
| C8×D424 | 2 |
| #20272769 | 2 |
| C53×#1370 | 2 |
| #12445 | 53 |