Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
254 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 254 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 |
|---|---|---|
| 14. #14581715 | C4 | semidirect |
| 106. C83 | #1927 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581723 | 2 |
| C2×#14581715 | 2 |
| #19127607 | 2 |
| #19127463 | 2 |
| #19127456 | 2 |
| C4×C4⋊C4×C83 | 2 |
| #1927 | 83 |