Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
406 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 75 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×#14581818 | C2 | semidirect |
| 2. #19128279 | C2 | semidirect |
| 3. C2×#14581719 | C2 | semidirect |
| 4. C2×#14581718 | C2 | semidirect |
| 5. #19127604 | C2 | semidirect |
| 6. #19127469 | C2 | semidirect |
| 7. C2×AGL(1,ℤ/8)×C83 | C2 | semidirect |
| 45. #13050574 | D4 | semidirect |
| 68. C2×D4×C83 | D4 | semidirect |
| 74. M16×C83 | D4 | semidirect |
| 153. C83 | #2006 | semidirect |
| 155. C2×AGL(1,ℤ/8) | D83 | semidirect |
| 205. C2×D4 | C22⋊D83 | semidirect |
| 218. M16 | C22⋊D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581818 | 2 |
| #19128279 | 2 |
| C2×#14581719 | 2 |
| C2×#14581718 | 2 |
| #19127604 | 2 |
| #19127469 | 2 |
| C2×AGL(1,ℤ/8)×C83 | 2 |
| #2006 | 83 |