Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
816 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 229 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 |
|---|---|---|
| 2. C22×#13050573 | C2 | semidirect |
| 3. C2×C4⋊C4×D83 | C2 | semidirect |
| 4. #19127699 | C2 | direct (N × H) |
| 5. C2×#14581717 | C2 | semidirect |
| 6. C2×#14581715 | C2 | semidirect |
| 7. C2×#14581713 | C2 | semidirect |
| 8. C2×#102×C83 | C2 | semidirect |
| 11. C2×#13050589 | C4 | semidirect |
| 19. C2×#13050573 | C22 | semidirect |
| 24. C4⋊C4×D83 | C22 | semidirect |
| 25. #14581717 | C22 | semidirect |
| 26. #14581715 | C22 | semidirect |
| 27. #14581713 | C22 | semidirect |
| 31. #102×C83 | C22 | semidirect |
| 35. #13050589 | C2×C4 | semidirect |
| 38. C2×Dic166 | C2×C4 | semidirect |
| 62. C2×D4×C83 | C2×C4 | semidirect |
| 81. D4×C83 | C22×C4 | semidirect |
| 102. Dic166 | C22×C4 | semidirect |
| 125. C2×C83 | #417 | semidirect |
| 131. C83 | C2×#417 | semidirect |
| 139. C2×#102 | D83 | semidirect |
| 162. #102 | C2×D83 | semidirect |
| 176. C2×D4 | C4×D83 | semidirect |
| 216. D4 | C2×C4×D83 | semidirect |
| 257. C2 | #19127699 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13050589 | 2 |
| C22×#13050573 | 2 |
| C2×C4⋊C4×D83 | 2 |
| #19127699 | 2 |
| C2×#14581717 | 2 |
| C2×#14581715 | 2 |
| C2×#14581713 | 2 |
| C2×#102×C83 | 2 |
| C2×#417 | 83 |