Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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. #19128323 | C2 | semidirect |
| 2. #19128105 | C2 | semidirect |
| 3. #19128086 | C2 | semidirect |
| 4. #19128062 | C2 | semidirect |
| 5. #19127950 | C2 | semidirect |
| 6. #19127939 | C2 | semidirect |
| 8. #19127799 | C2 | semidirect |
| 9. C4×D664 | C2 | semidirect |
| 10. #19127655 | C2 | semidirect |
| 11. C4×Q16×C83 | C2 | semidirect |
| 118. C83 | #3175 | semidirect |
| 127. C4×Q16 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128323 | 2 |
| #19128105 | 2 |
| #19128086 | 2 |
| #19128062 | 2 |
| #19127950 | 2 |
| #19127939 | 2 |
| #19127938 | 2 |
| #19127799 | 2 |
| C4×D664 | 2 |
| #19127655 | 2 |
| C4×Q16×C83 | 2 |
| #3175 | 83 |