Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
324 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 60. Q16×C83 | Q8 | semidirect |
| 103. C83 | #3383 | semidirect |
| 145. Q16 | Dic166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128427 | 2 |
| #19128105 | 2 |
| #19128103 | 2 |
| #19128102 | 2 |
| #19128008 | 2 |
| #19128006 | 2 |
| #19127984 | 2 |
| C8×Dic166 | 2 |
| Q16×Dic83 | 2 |
| C4×Q16×C83 | 2 |
| #3383 | 83 |