Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
346 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 93 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. #19128176 | C2 | semidirect |
| 2. #19127718 | C2 | semidirect |
| 3. #19127706 | C2 | semidirect |
| 4. #19127675 | C2 | semidirect |
| 5. #19127472 | C2 | semidirect |
| 6. #19127458 | C2 | semidirect |
| 22. C2×SD16×C83 | C4 | semidirect |
| 23. C2×D8×C83 | C4 | semidirect |
| 44. C2×Q8×C83 | C2×C4 | semidirect |
| 50. C2×D4×C83 | C2×C4 | semidirect |
| 59. C2×C8×C83 | C2×C4 | semidirect |
| 116. C83 | #1904 | semidirect |
| 128. C2×SD16 | Dic83 | semidirect |
| 129. C2×D8 | Dic83 | semidirect |
| 146. C2×Q8 | C2×Dic83 | semidirect |
| 152. C2×D4 | C2×Dic83 | semidirect |
| 165. C2×C8 | C2×Dic83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128176 | 2 |
| #19127718 | 2 |
| #19127706 | 2 |
| #19127675 | 2 |
| #19127472 | 2 |
| #19127458 | 2 |
| C2×AGL(1,ℤ/8)×C83 | 2 |
| #1904 | 83 |