Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
412 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 99 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×#14581750 | C2 | semidirect |
| 3. C2×#14581714 | C2 | semidirect |
| 4. C2×#14581712 | C2 | semidirect |
| 5. C2×(C2×D83)⋊C8 | C2 | semidirect |
| 6. #19127463 | C2 | semidirect |
| 7. #340×C83 | C2 | semidirect |
| 13. #14581767 | C4 | semidirect |
| 49. C4⋊Dic83 | D4 | semidirect |
| 62. C4⋊C4×C83 | D4 | semidirect |
| 146. C83 | #1875 | semidirect |
| 153. #340 | D83 | semidirect |
| 205. C4⋊C4 | D332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581767 | 2 |
| C2×#14581750 | 2 |
| C2×#14581714 | 2 |
| C2×#14581712 | 2 |
| C2×(C2×D83)⋊C8 | 2 |
| #19127463 | 2 |
| #340×C83 | 2 |
| #1875 | 83 |