Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
564 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 181 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. C22×#13050579 | C2 | semidirect |
| 2. C2×#14581771 | C2 | semidirect |
| 4. #19127930 | C2 | direct (N × H) |
| 5. C2×#14581724 | C2 | semidirect |
| 6. C2×#14581717 | C2 | semidirect |
| 7. C2×#14581714 | C2 | semidirect |
| 8. C23×C8×C83 | C2 | semidirect |
| 13. C2×#13050579 | C22 | semidirect |
| 15. #14581771 | C22 | semidirect |
| 23. #14581724 | C22 | semidirect |
| 24. #14581717 | C22 | semidirect |
| 25. #14581714 | C22 | semidirect |
| 30. C22×C8×C83 | C22 | semidirect |
| 62. C2×C8×C83 | D4 | semidirect |
| 67. C23×C83 | SD16 | semidirect |
| 97. C8×C83 | C2×D4 | semidirect |
| 103. C22×C83 | C2×SD16 | semidirect |
| 118. C2×C83 | #465 | semidirect |
| 124. C83 | C2×#465 | semidirect |
| 126. C23×C8 | D83 | semidirect |
| 142. C22×C8 | C2×D83 | semidirect |
| 179. C2×C8 | C22⋊D83 | semidirect |
| 195. C23 | #13050579 | semidirect |
| 221. C8 | C2×C22⋊D83 | semidirect |
| 231. C22 | C2×#13050579 | semidirect |
| 243. C2 | #19127930 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13050579 | 2 |
| C2×#14581771 | 2 |
| C2×#14581766 | 2 |
| #19127930 | 2 |
| C2×#14581724 | 2 |
| C2×#14581717 | 2 |
| C2×#14581714 | 2 |
| C23×C8×C83 | 2 |
| C2×#465 | 83 |