Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
326 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 125 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. #19128106 | C2 | semidirect |
| 4. #19128099 | C2 | semidirect |
| 5. #19128052 | C2 | semidirect |
| 6. #19128052 | C2 | semidirect |
| 8. #19128009 | C2 | semidirect |
| 103. C83 | #3231 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128258 | 2 |
| #19128106 | 2 |
| #19128099 | 2 |
| #19128052 | 2 |
| #19128043 | 2 |
| #19128009 | 2 |
| #431×C83 | 2 |
| #3231 | 83 |