Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
376 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 143 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 |
| 72. C2×Q8×C83 | Q8 | semidirect |
| 130. C83 | #3078 | semidirect |
| 177. C2×Q8 | Dic166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128254 | 2 |
| C2×Q8×Dic83 | 2 |
| #19128010 | 2 |
| #19128006 | 2 |
| #19127994 | 2 |
| #19127984 | 2 |
| #19127744 | 2 |
| #19127743 | 2 |
| #19127724 | 2 |
| #19127710 | 2 |
| #419×C83 | 2 |
| #3078 | 83 |