Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
220 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 220 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 |
|---|---|---|
| 3. #19127505 | C2 | semidirect |
| 13. C2×Q16×C83 | C4 | semidirect |
| 59. C83 | #2141 | semidirect |
| 67. C2×Q16 | Dic83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581732 | 2 |
| #19127739 | 2 |
| #19127505 | 2 |
| C22×Q16×C83 | 2 |
| #2141 | 83 |