Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
412 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 3. #20274765 | C2 | semidirect |
| 4. #20272837 | C2 | semidirect |
| 5. C53×#1813 | C2 | semidirect |
| 172. #1813 | D53 | semidirect |
| 199. C53 | #12810 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283431 | 2 |
| #20276398 | 2 |
| #20274765 | 2 |
| #20272837 | 2 |
| C53×#1813 | 2 |
| #12810 | 53 |