Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
220 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 49 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. #19128506 | C2 | semidirect |
| 2. #19128137 | C2 | semidirect |
| 3. C2×#14581733 | C2 | semidirect |
| 4. #19127513 | C2 | semidirect |
| 5. #19127507 | C2 | semidirect |
| 6. #19127485 | C2 | semidirect |
| 7. #472×C83 | C2 | semidirect |
| 18. #14581732 | C22 | semidirect |
| 19. C2×C83⋊C16 | C22 | semidirect |
| 21. C2×D8×C83 | C22 | semidirect |
| 23. #108×C83 | C22 | semidirect |
| 94. C83 | #2192 | semidirect |
| 98. #472 | D83 | semidirect |
| 110. C2×D8 | C2×D83 | semidirect |
| 117. #108 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128506 | 2 |
| #19128137 | 2 |
| C2×#14581733 | 2 |
| #19127513 | 2 |
| #19127507 | 2 |
| #19127485 | 2 |
| #472×C83 | 2 |
| #2192 | 83 |