Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
572 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 157 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×#14581812 | C2 | semidirect |
| 2. #19128251 | C2 | semidirect |
| 3. #19128083 | C2 | semidirect |
| 4. #19128080 | C2 | semidirect |
| 5. #19128077 | C2 | semidirect |
| 6. #19128075 | C2 | semidirect |
| 7. #19128073 | C2 | semidirect |
| 8. C2×C4×C83⋊C8 | C2 | semidirect |
| 9. #532×C83 | C2 | semidirect |
| 42. C2×C83⋊C8 | D4 | semidirect |
| 93. C4×C83 | #135 | semidirect |
| 102. C83 | #3147 | semidirect |
| 105. #532 | D83 | semidirect |
| 196. C4 | #14581812 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581812 | 2 |
| #19128251 | 2 |
| #19128083 | 2 |
| #19128080 | 2 |
| #19128077 | 2 |
| #19128075 | 2 |
| #19128073 | 2 |
| C2×C4×C83⋊C8 | 2 |
| #532×C83 | 2 |
| #3147 | 83 |