Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
296 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 296 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 |
|---|---|---|
| 2. C2×#14581728 | C2 | semidirect |
| 3. #19127709 | C2 | semidirect |
| 5. C2×#14581710 | C2 | semidirect |
| 7. #405×C83 | C2 | semidirect |
| 13. C2×#13050579 | C4 | semidirect |
| 107. C83 | #1977 | semidirect |
| 114. #405 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13050579 | 2 |
| C2×#14581728 | 2 |
| #19127709 | 2 |
| #19127705 | 2 |
| C2×#14581710 | 2 |
| C2×#14581708 | 2 |
| #405×C83 | 2 |
| #1977 | 83 |