Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
536 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 536 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 |
|---|---|---|
| 4. #19127740 | C2 | direct (N × H) |
| 5. C2×#14581726 | C2 | semidirect |
| 6. C2×#14581725 | C2 | semidirect |
| 7. C2×#14581723 | C2 | semidirect |
| 8. C2×#106×C83 | C2 | semidirect |
| 11. C2×#13050573 | C4 | semidirect |
| 23. #14581726 | C22 | semidirect |
| 24. #14581725 | C22 | semidirect |
| 25. #14581723 | C22 | semidirect |
| 29. #106×C83 | C22 | semidirect |
| 40. #13050573 | C2×C4 | semidirect |
| 41. C2×C83⋊C8 | C2×C4 | semidirect |
| 53. C2×C8×C83 | C2×C4 | semidirect |
| 82. C8×C83 | C22×C4 | semidirect |
| 83. C83⋊C8 | C22×C4 | semidirect |
| 100. C2×C83 | #428 | semidirect |
| 106. C83 | C2×#428 | semidirect |
| 114. C2×#106 | D83 | semidirect |
| 135. #106 | C2×D83 | semidirect |
| 152. C2×C8 | C4×D83 | semidirect |
| 189. C8 | C2×C4×D83 | semidirect |
| 207. C2 | #19127740 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13050573 | 2 |
| C2×#14581750 | 2 |
| C2×C4⋊C4×D83 | 2 |
| #19127740 | 2 |
| C2×#14581726 | 2 |
| C2×#14581725 | 2 |
| C2×#14581723 | 2 |
| C2×#106×C83 | 2 |
| C2×#428 | 83 |