Finite Group DatabasebetaFinite Group DatabasebetaOrder 34624.
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 1. #31772621 | C2 | semidirect |
| 2. #31772619 | C2 | semidirect |
| 3. #31772615 | C2 | semidirect |
| 4. #31772610 | C2 | semidirect |
| 5. #31772608 | C2 | semidirect |
| 7. C4×Dic1082 | C2 | semidirect |
| 8. C4×C22⋊D541 | C2 | semidirect |
| 9. #31772587 | C2 | semidirect |
| 10. C42×D541 | C2 | semidirect |
| 11. C4×D4×C541 | C2 | semidirect |
| 74. C541 | #529 | semidirect |
| 84. C4×D4 | D541 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31772621 | 2 |
| #31772619 | 2 |
| #31772615 | 2 |
| #31772610 | 2 |
| #31772608 | 2 |
| #31772599 | 2 |
| C4×Dic1082 | 2 |
| C4×C22⋊D541 | 2 |
| #31772587 | 2 |
| C42×D541 | 2 |
| C4×D4×C541 | 2 |
| #529 | 541 |