Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
336 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 129 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×#14581703 | C2 | semidirect |
| 4. #19127455 | C2 | semidirect |
| 5. C2×C4×C8×C83 | C2 | semidirect |
| 13. (C2×D83)⋊C8 | C4 | semidirect |
| 78. C83 | #1750 | semidirect |
| 82. C2×C4×C8 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581749 | 2 |
| C2×(C2×D83)⋊C8 | 2 |
| C2×#14581703 | 2 |
| #19127455 | 2 |
| C2×C4×C8×C83 | 2 |
| #1750 | 83 |