Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
402 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 3. C2×#14581716 | C2 | semidirect |
| 5. #19127463 | C2 | semidirect |
| 6. #19127456 | C2 | semidirect |
| 7. #391×C83 | C2 | semidirect |
| 12. C2×#13050577 | C4 | semidirect |
| 43. C2×C83⋊C8 | C2×C4 | semidirect |
| 52. C2×Q8×C83 | C2×C4 | semidirect |
| 85. C2×C4×C83 | SD16 | semidirect |
| 134. C83 | #1877 | semidirect |
| 139. #391 | D83 | semidirect |
| 166. C2×Q8 | C4×D83 | semidirect |
| 227. C2×C4 | #13050577 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13050577 | 2 |
| C2×C4×D332 | 2 |
| C2×#14581716 | 2 |
| C2×#14581712 | 2 |
| #19127463 | 2 |
| #19127456 | 2 |
| #391×C83 | 2 |
| #1877 | 83 |