Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
512 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14581784 | C2 | semidirect |
| 2. #19127637 | C2 | semidirect |
| 3. #19127632 | C2 | semidirect |
| 4. #19127626 | C2 | semidirect |
| 6. #19127574 | C2 | semidirect |
| 7. #19127569 | C2 | semidirect |
| 95. C83 | #2633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581784 | 2 |
| #19127637 | 2 |
| #19127632 | 2 |
| #19127626 | 2 |
| #19127615 | 2 |
| #19127574 | 2 |
| #19127569 | 2 |
| C2×C4×D4×C83 | 2 |
| #2633 | 83 |