Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
372 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 123 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. Q8×D332 | C2 | semidirect |
| 2. #19128060 | C2 | semidirect |
| 3. #19128051 | C2 | semidirect |
| 4. #19127996 | C2 | semidirect |
| 5. #19127981 | C2 | semidirect |
| 7. #19127903 | C2 | semidirect |
| 8. #19127832 | C2 | semidirect |
| 9. #19127799 | C2 | semidirect |
| 11. #556×C83 | C2 | semidirect |
| 123. C83 | #3367 | semidirect |
| 124. #556 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D332 | 2 |
| #19128060 | 2 |
| #19128051 | 2 |
| #19127996 | 2 |
| #19127981 | 2 |
| #19127913 | 2 |
| #19127903 | 2 |
| #19127832 | 2 |
| #19127799 | 2 |
| C4×#13050575 | 2 |
| #556×C83 | 2 |
| #3367 | 83 |