Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
368 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 2. #19128106 | C2 | semidirect |
| 3. #19128081 | C2 | semidirect |
| 4. #19128052 | C2 | semidirect |
| 6. C4×Dic332 | C2 | semidirect |
| 48. C2×C4×C83 | Q16 | semidirect |
| 78. C83 | #3170 | semidirect |
| 130. C2×C4 | Dic332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128258 | 2 |
| #19128106 | 2 |
| #19128081 | 2 |
| #19128052 | 2 |
| #19127942 | 2 |
| C4×Dic332 | 2 |
| C2×C4×C8×C83 | 2 |
| #3170 | 83 |