Finite Group DatabasebetaFinite Group DatabasebetaOrder 34624.
258 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 107 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. #31772675 | C2 | semidirect |
| 2. #31772674 | C2 | semidirect |
| 3. #31772661 | C2 | semidirect |
| 4. #31772656 | C2 | semidirect |
| 5. #31772650 | C2 | semidirect |
| 6. C2×#22575825 | C2 | semidirect |
| 7. #131×C541 | C2 | semidirect |
| 10. #22575836 | C22 | semidirect |
| 12. C2×Dic1082 | C22 | semidirect |
| 16. Dic2164 | C22 | semidirect |
| 17. #22575825 | C22 | semidirect |
| 18. #22575825 | C22 | semidirect |
| 19. #22575825 | C22 | semidirect |
| 20. D4328 | C22 | semidirect |
| 22. M16×C541 | C22 | semidirect |
| 23. C2×C8×C541 | C22 | semidirect |
| 53. C541 | #577 | semidirect |
| 61. #131 | D541 | semidirect |
| 76. M16 | C2×D541 | semidirect |
| 77. C2×C8 | C2×D541 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31772675 | 2 |
| #31772674 | 2 |
| #31772661 | 2 |
| #31772656 | 2 |
| #31772650 | 2 |
| C2×#22575825 | 2 |
| #131×C541 | 2 |
| #577 | 541 |