Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
140 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 47 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. #19127526 | C2 | semidirect |
| 4. #19127506 | C2 | semidirect |
| 5. #19127504 | C2 | semidirect |
| 7. #366×C83 | C2 | semidirect |
| 67. C83 | #2236 | semidirect |
| 71. #366 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19127943 | 2 |
| #107×D83 | 2 |
| #19127526 | 2 |
| #19127506 | 2 |
| #19127504 | 2 |
| (C2×D83)⋊C16 | 2 |
| #366×C83 | 2 |
| #2236 | 83 |