Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
210 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 55 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. #19128429 | C2 | semidirect |
| 4. #19127448 | C2 | semidirect |
| 5. Q8⋊(C83⋊C8) | C2 | semidirect |
| 6. #19127431 | C2 | semidirect |
| 68. Dic166 | SD16 | semidirect |
| 91. C83 | #1626 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128429 | 2 |
| #19128047 | 2 |
| #19127898 | 2 |
| #19127448 | 2 |
| Q8⋊(C83⋊C8) | 2 |
| #19127431 | 2 |
| #460×C83 | 2 |
| #1626 | 83 |