Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
364 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 117 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. #19128417 | C2 | semidirect |
| 2. #19128028 | C2 | semidirect |
| 3. #19127988 | C2 | semidirect |
| 4. #19127938 | C2 | semidirect |
| 5. C4×D664 | C2 | semidirect |
| 6. C8×D332 | C2 | semidirect |
| 7. #19127738 | C2 | semidirect |
| 8. #500×C83 | C2 | semidirect |
| 88. C83 | #3341 | semidirect |
| 90. #500 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128417 | 2 |
| #19128028 | 2 |
| #19127988 | 2 |
| #19127938 | 2 |
| C4×D664 | 2 |
| C8×D332 | 2 |
| #19127738 | 2 |
| #500×C83 | 2 |
| #3341 | 83 |