Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
488 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#14581784 | C2 | semidirect |
| 3. #19128066 | C2 | direct (N × H) |
| 4. C2×#14581714 | C2 | semidirect |
| 5. C2×#97×C83 | C2 | semidirect |
| 11. #14581784 | C22 | semidirect |
| 14. #14581714 | C22 | semidirect |
| 17. #97×C83 | C22 | semidirect |
| 59. C2×C83 | #490 | semidirect |
| 64. C83 | C2×#490 | semidirect |
| 69. C2×#97 | D83 | semidirect |
| 81. #97 | C2×D83 | semidirect |
| 124. C2 | #19128066 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581789 | 2 |
| C2×#14581784 | 2 |
| #19128066 | 2 |
| C2×#14581714 | 2 |
| C2×#97×C83 | 2 |
| C2×#490 | 83 |