Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
406 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 406 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×#14581792 | C2 | semidirect |
| 3. C2×#14581717 | C2 | semidirect |
| 5. #336×C83 | C2 | semidirect |
| 49. C2×C4×C83 | SD16 | semidirect |
| 88. C83 | #2013 | semidirect |
| 93. #336 | D83 | semidirect |
| 148. C2×C4 | #13050579 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13050579 | 2 |
| C2×#14581792 | 2 |
| C2×#14581717 | 2 |
| #19127603 | 2 |
| #336×C83 | 2 |
| #2013 | 83 |