Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
732 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 165 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. C2×#14581817 | C2 | semidirect |
| 2. C22×#13050577 | C2 | semidirect |
| 3. #19128265 | C2 | semidirect |
| 4. #19127846 | C2 | semidirect |
| 5. #19127840 | C2 | semidirect |
| 6. #19127710 | C2 | semidirect |
| 7. #19127697 | C2 | semidirect |
| 8. #19127668 | C2 | semidirect |
| 9. C2×2−1+4×C83 | C2 | semidirect |
| 23. #14581716 | C22 | semidirect |
| 24. #14581716 | C22 | semidirect |
| 25. #14581713 | C22 | semidirect |
| 26. C22⋊(C83⋊C8) | C22 | semidirect |
| 33. C2×#41×C83 | C22 | semidirect |
| 36. C22×Q8×C83 | C22 | semidirect |
| 61. #41×C83 | D4 | semidirect |
| 69. C2×Q8×C83 | D4 | semidirect |
| 146. C83 | #3010 | semidirect |
| 147. C2×2−1+4 | D83 | semidirect |
| 162. C2×#41 | C2×D83 | semidirect |
| 165. C22×Q8 | C2×D83 | semidirect |
| 191. #41 | C22⋊D83 | semidirect |
| 199. C2×Q8 | C22⋊D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581817 | 2 |
| C22×#13050577 | 2 |
| #19128265 | 2 |
| #19127846 | 2 |
| #19127840 | 2 |
| #19127710 | 2 |
| #19127697 | 2 |
| #19127668 | 2 |
| C2×2−1+4×C83 | 2 |
| #3010 | 83 |