Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
434 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 434 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. #19128252 | C2 | semidirect |
| 2. C4×#13050589 | C2 | semidirect |
| 3. #19128027 | C2 | semidirect |
| 4. #19127993 | C2 | semidirect |
| 5. #19127902 | C2 | semidirect |
| 6. #19127896 | C2 | semidirect |
| 7. #19127847 | C2 | semidirect |
| 8. #19127788 | C2 | semidirect |
| 9. #19127781 | C2 | semidirect |
| 10. #19127753 | C2 | semidirect |
| 11. #476×C83 | C2 | semidirect |
| 88. D4×C83 | #41 | semidirect |
| 114. Dic166 | #41 | semidirect |
| 145. C83 | #3106 | semidirect |
| 150. #476 | D83 | semidirect |
| 241. D4 | #13050591 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128252 | 2 |
| C4×#13050589 | 2 |
| #19128027 | 2 |
| #19127993 | 2 |
| #19127902 | 2 |
| #19127896 | 2 |
| #19127847 | 2 |
| #19127788 | 2 |
| #19127781 | 2 |
| #19127753 | 2 |
| #476×C83 | 2 |
| #3106 | 83 |