Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
320 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 53. Q16×C83 | Q8 | semidirect |
| 91. C83 | #3390 | semidirect |
| 129. Q16 | Dic166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128427 | 2 |
| #19128109 | 2 |
| #19128103 | 2 |
| #19128010 | 2 |
| #19128008 | 2 |
| #19127994 | 2 |
| #19127831 | 2 |
| #19127808 | 2 |
| C4×Q16×C83 | 2 |
| #3390 | 83 |