Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
436 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 436 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. C4×#13133153 | C2 | semidirect |
| 3. #20273306 | C2 | semidirect |
| 4. #20273131 | C2 | semidirect |
| 5. C53×#1451 | C2 | semidirect |
| 134. #1451 | D53 | semidirect |
| 158. C53 | #9726 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285294 | 2 |
| C4×#13133153 | 2 |
| #20273306 | 2 |
| #20273131 | 2 |
| C53×#1451 | 2 |
| #9726 | 53 |