Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
146 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 1. #19128119 | C2 | semidirect |
| 3. #19127486 | C2 | semidirect |
| 4. C4×C83⋊C16 | C2 | semidirect |
| 5. #364×C83 | C2 | semidirect |
| 51. C83 | #2170 | semidirect |
| 54. #364 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128119 | 2 |
| #19127819 | 2 |
| #19127486 | 2 |
| C4×C83⋊C16 | 2 |
| #364×C83 | 2 |
| #2170 | 83 |