Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
376 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 3. #19128007 | C2 | semidirect |
| 4. #19128006 | C2 | semidirect |
| 5. #19127993 | C2 | semidirect |
| 6. #19127987 | C2 | semidirect |
| 7. #19127986 | C2 | semidirect |
| 11. #477×C83 | C2 | semidirect |
| 47. Q8×D83 | Q8 | semidirect |
| 131. C83 | #3078 | semidirect |
| 137. #477 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128256 | 2 |
| C4×Q8×D83 | 2 |
| #19128007 | 2 |
| #19128006 | 2 |
| #19127993 | 2 |
| #19127987 | 2 |
| #19127986 | 2 |
| #19127742 | 2 |
| #19127723 | 2 |
| #19127708 | 2 |
| #477×C83 | 2 |
| #3078 | 83 |