Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
750 conjugacy classes of subgroups; only the 199 normal subgroups are shown.
This group has 750 conjugacy classes of subgroups — too many to draw. Only its 199 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. #20274325 | C2 | semidirect |
| 4. #20274324 | C2 | semidirect |
| 5. #20274323 | C2 | semidirect |
| 7. C53×#1710 | C2 | semidirect |
| 103. #1710 | D53 | direct (N × H) |
| 107. D53 | #1710 | direct (N × H) |
| 125. C53 | C2×#1710 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #500×D53 | 2 |
| #487×D53 | 2 |
| #20274325 | 2 |
| #20274324 | 2 |
| #20274323 | 2 |
| C82×D53 | 2 |
| C53×#1710 | 2 |
| C2×#1710 | 53 |