Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
382 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 382 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. #19128272 | C2 | semidirect |
| 2. C2×#14581779 | C2 | semidirect |
| 3. C2×#14581719 | C2 | semidirect |
| 4. #19127706 | C2 | semidirect |
| 5. C2×#14581710 | C2 | semidirect |
| 6. #19127462 | C2 | semidirect |
| 131. C83 | #2003 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128272 | 2 |
| C2×#14581779 | 2 |
| C2×#14581719 | 2 |
| #19127706 | 2 |
| C2×#14581710 | 2 |
| #19127462 | 2 |
| C2×AGL(1,ℤ/8)×C83 | 2 |
| #2003 | 83 |