Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
374 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 374 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 |
|---|---|---|
| 1. #19128411 | C2 | semidirect |
| 2. Q8×D332 | C2 | semidirect |
| 3. #19128110 | C2 | semidirect |
| 4. #19128099 | C2 | semidirect |
| 5. #19128002 | C2 | semidirect |
| 6. #19127992 | C2 | semidirect |
| 7. #19127992 | C2 | semidirect |
| 8. #19127982 | C2 | semidirect |
| 11. #446×C83 | C2 | semidirect |
| 51. D664 | Q8 | semidirect |
| 88. D332 | C2×Q8 | semidirect |
| 98. C8×C83 | C2×Q8 | semidirect |
| 122. C83 | #3384 | semidirect |
| 131. #446 | D83 | semidirect |
| 220. C8 | Q8×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128411 | 2 |
| Q8×D332 | 2 |
| #19128110 | 2 |
| #19128099 | 2 |
| #19128002 | 2 |
| #19127992 | 2 |
| #19127982 | 2 |
| #19127814 | 2 |
| C4×D664 | 2 |
| #446×C83 | 2 |
| #3384 | 83 |