Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
316 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 85 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×#14581725 | C2 | semidirect |
| 3. C2×#14581717 | C2 | semidirect |
| 4. C2×#14581715 | C2 | semidirect |
| 7. #340×C83 | C2 | semidirect |
| 130. C83 | #2036 | semidirect |
| 137. #340 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581772 | 2 |
| C2×#14581725 | 2 |
| C2×#14581717 | 2 |
| C2×#14581715 | 2 |
| C2×(C2×D83)⋊C8 | 2 |
| #19127558 | 2 |
| #340×C83 | 2 |
| #2036 | 83 |