Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
360 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 133 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. #19128111 | C2 | semidirect |
| 3. #19128104 | C2 | semidirect |
| 5. #19127996 | C2 | semidirect |
| 6. #19127986 | C2 | semidirect |
| 8. #19127832 | C2 | semidirect |
| 11. #557×C83 | C2 | semidirect |
| 47. #13050577 | Q8 | semidirect |
| 77. Q8×C83 | C2×Q8 | semidirect |
| 96. C83⋊C8 | C2×Q8 | semidirect |
| 117. C83 | #3386 | semidirect |
| 118. #557 | D83 | semidirect |
| 196. Q8 | Q8×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D332 | 2 |
| #19128111 | 2 |
| #19128104 | 2 |
| #19127998 | 2 |
| #19127996 | 2 |
| #19127986 | 2 |
| #19127978 | 2 |
| #19127832 | 2 |
| #19127799 | 2 |
| C4×#13050577 | 2 |
| #557×C83 | 2 |
| #3386 | 83 |