Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
164 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 57 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×#14581737 | C2 | semidirect |
| 2. #19127942 | C2 | semidirect |
| 4. #19127529 | C2 | semidirect |
| 5. #19127506 | C2 | semidirect |
| 6. #19127503 | C2 | semidirect |
| 7. C22×C16×C83 | C2 | semidirect |
| 39. C16×C83 | D4 | semidirect |
| 59. C22×C83 | SD32 | semidirect |
| 76. C83 | #2217 | semidirect |
| 78. C22×C16 | D83 | semidirect |
| 115. C16 | C22⋊D83 | semidirect |
| 138. C22 | #14581737 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581737 | 2 |
| #19127942 | 2 |
| #19127937 | 2 |
| #19127529 | 2 |
| #19127506 | 2 |
| #19127503 | 2 |
| C22×C16×C83 | 2 |
| #2217 | 83 |