Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
216 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 61 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×#14581738 | C2 | semidirect |
| 3. #19127505 | C2 | semidirect |
| 53. C22×C83 | Q32 | semidirect |
| 66. C83 | #2188 | semidirect |
| 119. C22 | #14581738 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581738 | 2 |
| #19127942 | 2 |
| #19127505 | 2 |
| C22⋊(C83⋊C16) | 2 |
| C22×Q16×C83 | 2 |
| #2188 | 83 |