Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
228 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 2. C2×#14581731 | C2 | semidirect |
| 3. C2×C16×D83 | C2 | semidirect |
| 4. C22⋊(C83⋊C16) | C2 | semidirect |
| 5. (C2×D83)⋊C16 | C2 | semidirect |
| 6. (C2×D83)⋊C16 | C2 | semidirect |
| 7. C22⋊C16×C83 | C2 | semidirect |
| 93. C83 | #2113 | semidirect |
| 100. C22⋊C16 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581798 | 2 |
| C2×#14581731 | 2 |
| C2×C16×D83 | 2 |
| C22⋊(C83⋊C16) | 2 |
| (C2×D83)⋊C16 | 2 |
| C22⋊C16×C83 | 2 |
| #2113 | 83 |