Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
732 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14581839 | C2 | semidirect |
| 2. C22×#13050578 | C2 | semidirect |
| 3. #19128268 | C2 | semidirect |
| 4. #19127843 | C2 | semidirect |
| 5. #19127838 | C2 | semidirect |
| 6. #19127711 | C2 | semidirect |
| 7. #19127697 | C2 | semidirect |
| 8. #19127669 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C83 | C2 | semidirect |
| 15. C2×#13050589 | C22 | semidirect |
| 18. C2×Q8×D83 | C22 | semidirect |
| 27. #14581717 | C22 | semidirect |
| 28. #14581716 | C22 | semidirect |
| 29. #14581713 | C22 | semidirect |
| 30. (C2×D83)⋊C8 | C22 | semidirect |
| 48. C2×Dic166 | D4 | semidirect |
| 69. #41×C83 | D4 | semidirect |
| 146. C83 | #3010 | semidirect |
| 148. C2×AGL(1,ℤ/8) | D83 | semidirect |
| 191. #41 | C22⋊D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581839 | 2 |
| C22×#13050578 | 2 |
| #19128268 | 2 |
| #19127843 | 2 |
| #19127838 | 2 |
| #19127711 | 2 |
| #19127697 | 2 |
| #19127669 | 2 |
| C2×AGL(1,ℤ/8)×C83 | 2 |
| #3010 | 83 |