Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
482 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 131 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×#14581815 | C2 | semidirect |
| 2. C2×Q16×D83 | C2 | semidirect |
| 3. #19128363 | C2 | semidirect |
| 4. #19128085 | C2 | semidirect |
| 5. #19127943 | C2 | semidirect |
| 6. #19127938 | C2 | semidirect |
| 7. #19127923 | C2 | semidirect |
| 8. #19127866 | C2 | semidirect |
| 9. #19127841 | C2 | semidirect |
| 10. C8×D332 | C2 | semidirect |
| 11. C4×Q16×C83 | C2 | semidirect |
| 73. Q16×C83 | D4 | semidirect |
| 120. C2×D83 | #135 | semidirect |
| 137. C83 | #3285 | semidirect |
| 147. C4×Q16 | D83 | semidirect |
| 195. Q16 | D332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581815 | 2 |
| C2×Q16×D83 | 2 |
| #19128363 | 2 |
| #19128085 | 2 |
| #19127943 | 2 |
| #19127938 | 2 |
| #19127923 | 2 |
| #19127866 | 2 |
| #19127841 | 2 |
| C8×D332 | 2 |
| C4×Q16×C83 | 2 |
| #3285 | 83 |