Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
350 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 113 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. #19128514 | C2 | semidirect |
| 2. #19128143 | C2 | semidirect |
| 3. #19128142 | C2 | semidirect |
| 4. #19128134 | C2 | semidirect |
| 5. #19128133 | C2 | semidirect |
| 6. Q32×D83 | C2 | semidirect |
| 7. #19128117 | C2 | semidirect |
| 8. C2×Q32×C83 | C2 | semidirect |
| 82. C83 | #3417 | semidirect |
| 89. C2×Q32 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128514 | 2 |
| #19128143 | 2 |
| #19128142 | 2 |
| #19128134 | 2 |
| #19128133 | 2 |
| Q32×D83 | 2 |
| #19128117 | 2 |
| C2×Q32×C83 | 2 |
| #3417 | 83 |