Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
196 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 196 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×#14581737 | C2 | semidirect |
| 2. C2×#14581736 | C2 | semidirect |
| 3. C2×#14581735 | C2 | semidirect |
| 4. #19128079 | C2 | semidirect |
| 6. C16×Dic83 | C2 | semidirect |
| 7. C2×SD32×C83 | C2 | semidirect |
| 35. C83⋊C16 | D4 | semidirect |
| 43. C16×C83 | D4 | semidirect |
| 71. Dic83 | SD32 | semidirect |
| 77. C83 | #2248 | semidirect |
| 81. C2×SD32 | D83 | semidirect |
| 120. C16 | C22⋊D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581737 | 2 |
| C2×#14581736 | 2 |
| C2×#14581735 | 2 |
| #19128079 | 2 |
| #19128076 | 2 |
| C16×Dic83 | 2 |
| C2×SD32×C83 | 2 |
| #2248 | 83 |