Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 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 |
|---|---|---|
| 1. #19128306 | C2 | semidirect |
| 2. #19128103 | C2 | semidirect |
| 3. #19128078 | C2 | semidirect |
| 4. #19128066 | C2 | semidirect |
| 5. #19127954 | C2 | semidirect |
| 6. #19127937 | C2 | semidirect |
| 7. #19127814 | C2 | semidirect |
| 8. C4×D664 | C2 | semidirect |
| 9. #405×C83 | C2 | semidirect |
| 85. C83 | #3176 | semidirect |
| 94. #405 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128306 | 2 |
| #19128103 | 2 |
| #19128078 | 2 |
| #19128066 | 2 |
| #19127954 | 2 |
| #19127937 | 2 |
| #19127814 | 2 |
| C4×D664 | 2 |
| #405×C83 | 2 |
| #3176 | 83 |