Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
164 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 87 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. C2×#14581732 | C2 | semidirect |
| 2. C22×C83⋊C16 | C2 | semidirect |
| 3. C4⋊(C83⋊C16) | C2 | semidirect |
| 4. C22⋊(C83⋊C16) | C2 | semidirect |
| 5. C22⋊(C83⋊C16) | C2 | semidirect |
| 6. #19127477 | C2 | semidirect |
| 24. C83⋊C16 | D4 | semidirect |
| 62. C22×C83 | M32 | semidirect |
| 76. C83 | #2168 | semidirect |
| 138. C22 | #14581732 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581732 | 2 |
| C22×C83⋊C16 | 2 |
| C4⋊(C83⋊C16) | 2 |
| C22⋊(C83⋊C16) | 2 |
| #19127477 | 2 |
| C8×D4×C83 | 2 |
| #2168 | 83 |