Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
370 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 123 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. #19128426 | C2 | semidirect |
| 3. #19128050 | C2 | semidirect |
| 4. #19127984 | C2 | semidirect |
| 5. #19127983 | C2 | semidirect |
| 8. C8×Dic166 | C2 | semidirect |
| 11. #487×C83 | C2 | semidirect |
| 95. Dic166 | SD16 | semidirect |
| 119. C83 | #3359 | semidirect |
| 123. #487 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128426 | 2 |
| #19128366 | 2 |
| #19128050 | 2 |
| #19127984 | 2 |
| #19127983 | 2 |
| #19127905 | 2 |
| #19127903 | 2 |
| C8×Dic166 | 2 |
| C4×#13050579 | 2 |
| #19127786 | 2 |
| #487×C83 | 2 |
| #3359 | 83 |