Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
770 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 770 conjugacy classes of subgroups — too many to draw. Only its 171 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. #20275956 | C2 | semidirect |
| 4. #20275534 | C2 | semidirect |
| 5. #20274464 | C2 | semidirect |
| 6. C53×#2864 | C2 | semidirect |
| 91. #2864 | D53 | semidirect |
| 113. C53 | #30225 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283072 | 2 |
| #20275956 | 2 |
| #20275538 | 2 |
| #20275534 | 2 |
| #20274464 | 2 |
| C53×#2864 | 2 |
| #30225 | 53 |