Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 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 |
|---|---|---|
| 2. #19128051 | C2 | semidirect |
| 3. #19128039 | C2 | semidirect |
| 4. #19127996 | C2 | semidirect |
| 5. #19127949 | C2 | semidirect |
| 6. #19127903 | C2 | semidirect |
| 7. #19127840 | C2 | semidirect |
| 8. C4×#13050577 | C2 | semidirect |
| 9. #19127779 | C2 | semidirect |
| 10. #19127710 | C2 | semidirect |
| 11. D4×Q8×C83 | C2 | semidirect |
| 127. C83 | #3329 | semidirect |
| 129. D4×Q8 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128416 | 2 |
| #19128051 | 2 |
| #19128039 | 2 |
| #19127996 | 2 |
| #19127949 | 2 |
| #19127903 | 2 |
| #19127840 | 2 |
| C4×#13050577 | 2 |
| #19127779 | 2 |
| #19127710 | 2 |
| D4×Q8×C83 | 2 |
| #3329 | 83 |