Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
452 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 217 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. #19127779 | C2 | semidirect |
| 2. #19127754 | C2 | semidirect |
| 3. #19127665 | C2 | semidirect |
| 5. C2×#13050574 | C22 | semidirect |
| 6. C4⋊(C83⋊C8) | C22 | semidirect |
| 8. C22⋊(C83⋊C8) | C22 | semidirect |
| 9. C4×C83⋊C8 | C22 | semidirect |
| 44. C2×C4×C83 | M16 | semidirect |
| 70. C83 | #2975 | semidirect |
| 114. C2×C4 | #13050574 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19127779 | 2 |
| #19127754 | 2 |
| #19127665 | 2 |
| C2×C4×D4×C83 | 2 |
| #2975 | 83 |