Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
368 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 117 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×#14581811 | C2 | semidirect |
| 3. #19128132 | C2 | direct (N × H) |
| 4. C2×#14581738 | C2 | semidirect |
| 5. C2×#14581737 | C2 | semidirect |
| 6. C2×#14581733 | C2 | semidirect |
| 7. C2×C16×D83 | C2 | semidirect |
| 8. C2×SD32×C83 | C2 | semidirect |
| 12. #14581815 | C22 | semidirect |
| 14. #14581811 | C22 | semidirect |
| 20. #14581738 | C22 | semidirect |
| 21. #14581737 | C22 | semidirect |
| 22. #14581733 | C22 | semidirect |
| 24. C16×D83 | C22 | semidirect |
| 27. SD32×C83 | C22 | semidirect |
| 95. C2×C83 | #508 | semidirect |
| 100. C83 | C2×#508 | semidirect |
| 106. C2×SD32 | D83 | semidirect |
| 124. SD32 | C2×D83 | semidirect |
| 197. C2 | #19128132 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581815 | 2 |
| C2×#14581811 | 2 |
| #19128132 | 2 |
| C2×#14581738 | 2 |
| C2×#14581737 | 2 |
| C2×#14581733 | 2 |
| C2×C16×D83 | 2 |
| C2×SD32×C83 | 2 |
| C2×#508 | 83 |