Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
336 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 92. Dic166 | Q16 | semidirect |
| 113. C83 | #3363 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic166 | 2 |
| #19128429 | 2 |
| #19128052 | 2 |
| #19128050 | 2 |
| #19127996 | 2 |
| #19127995 | 2 |
| #19127911 | 2 |
| #19127909 | 2 |
| C8×Dic166 | 2 |
| #19127793 | 2 |
| C4×Q16×C83 | 2 |
| #3363 | 83 |