Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
254 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 65 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. #19127750 | C2 | semidirect |
| 4. #19127710 | C2 | semidirect |
| 6. #19127472 | C2 | semidirect |
| 7. C2×#101×C83 | C2 | semidirect |
| 106. C83 | #2049 | semidirect |
| 112. C2×#101 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581823 | 2 |
| #19127750 | 2 |
| #19127717 | 2 |
| #19127710 | 2 |
| #19127683 | 2 |
| #19127472 | 2 |
| C2×#101×C83 | 2 |
| #2049 | 83 |