Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
382 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 382 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. #19128430 | C2 | semidirect |
| 3. #19128064 | C2 | semidirect |
| 4. #19128048 | C2 | semidirect |
| 5. #19128000 | C2 | semidirect |
| 6. #19127981 | C2 | semidirect |
| 7. #19127901 | C2 | semidirect |
| 8. #19127899 | C2 | semidirect |
| 9. #19127831 | C2 | semidirect |
| 10. #19127804 | C2 | semidirect |
| 11. C4×SD16×C83 | C2 | semidirect |
| 77. Q8×C83 | #41 | semidirect |
| 125. C83 | #3368 | semidirect |
| 136. C4×SD16 | D83 | semidirect |
| 204. Q8 | #13050590 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128430 | 2 |
| #19128372 | 2 |
| #19128064 | 2 |
| #19128048 | 2 |
| #19128000 | 2 |
| #19127981 | 2 |
| #19127901 | 2 |
| #19127899 | 2 |
| #19127831 | 2 |
| #19127804 | 2 |
| C4×SD16×C83 | 2 |
| #3368 | 83 |