Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
384 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 3. #19128071 | C2 | semidirect |
| 4. #19128070 | C2 | semidirect |
| 5. #19128069 | C2 | semidirect |
| 6. #19128068 | C2 | semidirect |
| 9. #491×C83 | C2 | semidirect |
| 86. D83 | #491 | direct (N × H) |
| 88. C83 | C2×#491 | semidirect |
| 95. #491 | D83 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D83 | 2 |
| #125×D83 | 2 |
| #19128071 | 2 |
| #19128070 | 2 |
| #19128069 | 2 |
| #19128068 | 2 |
| #103×D83 | 2 |
| #97×D83 | 2 |
| #491×C83 | 2 |
| C2×#491 | 83 |