Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
494 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 149 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. #20274872 | C2 | semidirect |
| 4. #20274843 | C2 | semidirect |
| 5. C53×#1273 | C2 | semidirect |
| 107. #1273 | D53 | semidirect |
| 123. C53 | #10677 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20275521 | 2 |
| #20274872 | 2 |
| #20274843 | 2 |
| C53×#1273 | 2 |
| #10677 | 53 |