Finite Group DatabasebetaFinite Group DatabasebetaOrder 4544.
106 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 45 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. #14556136 | C2 | semidirect |
| 3. #14556135 | C2 | semidirect |
| 4. #14556063 | C2 | semidirect |
| 5. #14556056 | C2 | semidirect |
| 6. C4×C71⋊C8 | C2 | semidirect |
| 7. #104×C71 | C2 | semidirect |
| 9. #11765855 | C4 | semidirect |
| 10. #11765853 | C4 | semidirect |
| 11. #11765852 | C4 | semidirect |
| 12. #11765850 | C4 | semidirect |
| 51. C71 | #443 | semidirect |
| 58. #104 | D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14556148 | 2 |
| #14556136 | 2 |
| #14556135 | 2 |
| #14556063 | 2 |
| #14556056 | 2 |
| C4×C71⋊C8 | 2 |
| #104×C71 | 2 |
| #443 | 71 |