Finite Group DatabasebetaFinite Group DatabasebetaOrder 34624.
234 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 103 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. #31772622 | C2 | semidirect |
| 2. #31772620 | C2 | semidirect |
| 3. #31772616 | C2 | semidirect |
| 4. #31772611 | C2 | semidirect |
| 5. #31772607 | C2 | semidirect |
| 7. C4×Dic1082 | C2 | semidirect |
| 8. C4×D2164 | C2 | semidirect |
| 9. C4×C22⋊D541 | C2 | semidirect |
| 10. #31772585 | C2 | semidirect |
| 11. C2×C42×C541 | C2 | semidirect |
| 74. C541 | #529 | semidirect |
| 86. C2×C42 | D541 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31772622 | 2 |
| #31772620 | 2 |
| #31772616 | 2 |
| #31772611 | 2 |
| #31772607 | 2 |
| #31772602 | 2 |
| C4×Dic1082 | 2 |
| C4×D2164 | 2 |
| C4×C22⋊D541 | 2 |
| #31772585 | 2 |
| C2×C42×C541 | 2 |
| #529 | 541 |