Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
124 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 41 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. #19127523 | C2 | semidirect |
| 4. #19127518 | C2 | semidirect |
| 5. #19127516 | C2 | semidirect |
| 7. #365×C83 | C2 | semidirect |
| 62. C83 | #2239 | semidirect |
| 66. #365 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19127960 | 2 |
| #19127748 | 2 |
| #19127523 | 2 |
| #19127518 | 2 |
| #19127516 | 2 |
| #19127482 | 2 |
| #365×C83 | 2 |
| #2239 | 83 |