Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
210 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 53 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. #19128136 | C2 | semidirect |
| 2. C2×#14581735 | C2 | semidirect |
| 3. #19127971 | C2 | semidirect |
| 4. #19127517 | C2 | semidirect |
| 5. #19127508 | C2 | semidirect |
| 6. #19127485 | C2 | semidirect |
| 7. #578×C83 | C2 | semidirect |
| 91. C83 | #2193 | semidirect |
| 92. #578 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128136 | 2 |
| C2×#14581735 | 2 |
| #19127971 | 2 |
| #19127517 | 2 |
| #19127508 | 2 |
| #19127485 | 2 |
| #578×C83 | 2 |
| #2193 | 83 |