Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
220 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 57 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×#14581738 | C2 | semidirect |
| 2. C2×#14581736 | C2 | semidirect |
| 3. #19127942 | C2 | semidirect |
| 4. #19127505 | C2 | semidirect |
| 5. #19127502 | C2 | semidirect |
| 6. C22⋊(C83⋊C16) | C2 | semidirect |
| 86. C83 | #2189 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581738 | 2 |
| C2×#14581736 | 2 |
| #19127942 | 2 |
| #19127505 | 2 |
| #19127502 | 2 |
| C22⋊(C83⋊C16) | 2 |
| C2×#135×C83 | 2 |
| #2189 | 83 |