Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
362 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 3. #19128010 | C2 | semidirect |
| 4. #19128006 | C2 | semidirect |
| 5. #19127994 | C2 | semidirect |
| 6. #19127984 | C2 | semidirect |
| 65. C2×Q8×C83 | Q8 | semidirect |
| 117. C83 | #3082 | semidirect |
| 161. C2×Q8 | Dic166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128329 | 2 |
| #19128179 | 2 |
| #19128010 | 2 |
| #19128006 | 2 |
| #19127994 | 2 |
| #19127984 | 2 |
| #19127743 | 2 |
| #19127737 | 2 |
| #19127729 | 2 |
| C2×#14581716 | 2 |
| #419×C83 | 2 |
| #3082 | 83 |