Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
336 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 46. #13050580 | Q8 | semidirect |
| 90. Dic166 | Q16 | semidirect |
| 112. C83 | Q8×Q16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic166 | 2 |
| #19128431 | 2 |
| #19128105 | 2 |
| #19128104 | 2 |
| #19127997 | 2 |
| #19127995 | 2 |
| #19127994 | 2 |
| #19127825 | 2 |
| C4×#13050580 | 2 |
| #19127793 | 2 |
| #477×C83 | 2 |
| Q8×Q16 | 83 |