Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
460 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 460 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. #19128372 | C2 | semidirect |
| 2. #19128078 | C2 | semidirect |
| 3. #19128076 | C2 | semidirect |
| 4. #19127896 | C2 | semidirect |
| 5. #19127895 | C2 | semidirect |
| 6. C8×Dic166 | C2 | semidirect |
| 7. #19127783 | C2 | semidirect |
| 8. C4×D8×C83 | C2 | semidirect |
| 70. Dic166 | D8 | semidirect |
| 72. C8×C83 | #41 | semidirect |
| 94. C83 | #3391 | semidirect |
| 102. C4×D8 | D83 | semidirect |
| 167. C8 | #13050590 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128372 | 2 |
| #19128078 | 2 |
| #19128076 | 2 |
| #19127896 | 2 |
| #19127895 | 2 |
| C8×Dic166 | 2 |
| #19127783 | 2 |
| C4×D8×C83 | 2 |
| #3391 | 83 |