Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
392 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 141 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. #19128049 | C2 | semidirect |
| 3. #19127988 | C2 | semidirect |
| 4. #19127901 | C2 | semidirect |
| 5. Q8×C83⋊C8 | C2 | semidirect |
| 6. C4×#13050577 | C2 | semidirect |
| 7. Q82×C83 | C2 | semidirect |
| 46. Q8×C83 | SD16 | semidirect |
| 47. Q8×C83 | #41 | semidirect |
| 77. C83 | #3362 | semidirect |
| 78. Q82 | D83 | semidirect |
| 123. Q8 | #13050577 | semidirect |
| 124. Q8 | #13050591 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128373 | 2 |
| #19128049 | 2 |
| #19127988 | 2 |
| #19127901 | 2 |
| Q8×C83⋊C8 | 2 |
| C4×#13050577 | 2 |
| Q82×C83 | 2 |
| #3362 | 83 |