Finite Group DatabasebetaFinite Group DatabasebetaOrder 34624.
266 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 111 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. C2×#22575836 | C2 | semidirect |
| 2. #31772648 | C2 | direct (N × H) |
| 3. C2×#22575826 | C2 | semidirect |
| 4. C2×#22575824 | C2 | semidirect |
| 5. C2×#22575823 | C2 | semidirect |
| 6. C2×#22575821 | C2 | semidirect |
| 7. C22×#16864513 | C2 | semidirect |
| 8. C2×#41×C541 | C2 | semidirect |
| 10. #22575836 | C22 | semidirect |
| 15. #22575826 | C22 | semidirect |
| 16. #22575824 | C22 | semidirect |
| 17. #22575823 | C22 | semidirect |
| 18. #22575821 | C22 | semidirect |
| 21. C2×#16864513 | C22 | semidirect |
| 23. #41×C541 | C22 | semidirect |
| 66. C2×C541 | #135 | semidirect |
| 69. C541 | C2×#135 | semidirect |
| 72. C2×#41 | D541 | semidirect |
| 82. #41 | C2×D541 | semidirect |
| 137. C2 | #31772648 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575836 | 2 |
| #31772648 | 2 |
| C2×#22575826 | 2 |
| C2×#22575824 | 2 |
| C2×#22575823 | 2 |
| C2×#22575821 | 2 |
| C22×#16864513 | 2 |
| C2×#41×C541 | 2 |
| C2×#135 | 541 |