Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
410 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 121 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. #19128235 | C2 | semidirect |
| 2. C2×#14581780 | C2 | semidirect |
| 3. #19128085 | C2 | semidirect |
| 4. #19128056 | C2 | semidirect |
| 5. #19127924 | C2 | semidirect |
| 6. #19127917 | C2 | semidirect |
| 7. #19127859 | C2 | semidirect |
| 8. #19127854 | C2 | semidirect |
| 9. #19127842 | C2 | semidirect |
| 11. #431×C83 | C2 | semidirect |
| 14. C2×Dic332 | C22 | semidirect |
| 16. C2×#13050579 | C22 | semidirect |
| 19. #14581784 | C22 | semidirect |
| 24. #14581780 | C22 | semidirect |
| 28. C4×Dic166 | C22 | semidirect |
| 29. C4×D332 | C22 | semidirect |
| 34. #14581717 | C22 | semidirect |
| 35. #14581717 | C22 | semidirect |
| 39. C4⋊C8×C83 | C22 | semidirect |
| 42. C4×C8×C83 | C22 | semidirect |
| 144. C83 | #3211 | semidirect |
| 155. #431 | D83 | semidirect |
| 179. C4⋊C8 | C2×D83 | semidirect |
| 186. C4×C8 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128235 | 2 |
| C2×#14581780 | 2 |
| #19128085 | 2 |
| #19128056 | 2 |
| #19127924 | 2 |
| #19127917 | 2 |
| #19127859 | 2 |
| #19127854 | 2 |
| #19127842 | 2 |
| #19127837 | 2 |
| #431×C83 | 2 |
| #3211 | 83 |