Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
478 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 75 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×#14581817 | C2 | semidirect |
| 2. C2×#14581788 | C2 | semidirect |
| 3. C2×#14581719 | C2 | semidirect |
| 4. #19127705 | C2 | semidirect |
| 5. C2×#14581709 | C2 | semidirect |
| 6. #19127460 | C2 | semidirect |
| 7. #535×C83 | C2 | semidirect |
| 35. C2×D332 | D4 | semidirect |
| 44. #13050574 | D4 | semidirect |
| 48. C4×Dic83 | D4 | semidirect |
| 54. C2×Q8×C83 | D4 | semidirect |
| 63. C2×D4×C83 | D4 | semidirect |
| 66. C4⋊C4×C83 | D4 | semidirect |
| 139. C83 | #2002 | semidirect |
| 141. #535 | D83 | semidirect |
| 174. C2×Q8 | C22⋊D83 | semidirect |
| 191. C2×D4 | C22⋊D83 | semidirect |
| 203. C4⋊C4 | C22⋊D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581817 | 2 |
| C2×#14581788 | 2 |
| C2×#14581719 | 2 |
| #19127705 | 2 |
| C2×#14581709 | 2 |
| #19127460 | 2 |
| #535×C83 | 2 |
| #2002 | 83 |