Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 117 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. #19128437 | C2 | semidirect |
| 2. #19128408 | C2 | semidirect |
| 3. #19128054 | C2 | semidirect |
| 4. #19128047 | C2 | semidirect |
| 5. #19127999 | C2 | semidirect |
| 6. #19127997 | C2 | semidirect |
| 7. #19127914 | C2 | semidirect |
| 8. #19127825 | C2 | semidirect |
| 9. C4×#13050578 | C2 | semidirect |
| 10. D8×Dic83 | C2 | semidirect |
| 123. C83 | #3361 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128437 | 2 |
| #19128408 | 2 |
| #19128054 | 2 |
| #19128047 | 2 |
| #19127999 | 2 |
| #19127997 | 2 |
| #19127914 | 2 |
| #19127825 | 2 |
| C4×#13050578 | 2 |
| D8×Dic83 | 2 |
| #459×C83 | 2 |
| #3361 | 83 |