Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
326 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 69 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. #19127743 | C2 | semidirect |
| 3. #19127702 | C2 | semidirect |
| 4. C2×#14581708 | C2 | semidirect |
| 5. #19127603 | C2 | semidirect |
| 6. #19127461 | C2 | semidirect |
| 7. C2×#104×C83 | C2 | semidirect |
| 60. M16×C83 | D4 | semidirect |
| 131. C83 | #2037 | semidirect |
| 134. C2×#104 | D83 | semidirect |
| 181. M16 | C22⋊D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128265 | 2 |
| #19127743 | 2 |
| #19127702 | 2 |
| C2×#14581708 | 2 |
| #19127603 | 2 |
| #19127461 | 2 |
| C2×#104×C83 | 2 |
| #2037 | 83 |