Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
348 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 45. Q8×C83 | Q16 | semidirect |
| 70. C83 | #3395 | semidirect |
| 117. Q8 | #13050580 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128430 | 2 |
| #19128080 | 2 |
| #19127911 | 2 |
| #19127908 | 2 |
| Q8×C83⋊C8 | 2 |
| C4×#13050580 | 2 |
| #557×C83 | 2 |
| #3395 | 83 |