Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
278 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 97 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×#14581727 | C2 | semidirect |
| 4. #19127465 | C2 | semidirect |
| 71. C22×C83 | #108 | semidirect |
| 86. C83 | #1855 | semidirect |
| 157. C22 | #14581727 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581727 | 2 |
| #19127665 | 2 |
| C2×C22⋊(C83⋊C8) | 2 |
| #19127465 | 2 |
| C22×M16×C83 | 2 |
| #1855 | 83 |