Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
258 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 73 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. #19127675 | C2 | semidirect |
| 2. #19127496 | C2 | semidirect |
| 3. #19127494 | C2 | semidirect |
| 8. C2×#41×C83 | C4 | semidirect |
| 10. C4⋊Q8×C83 | C4 | semidirect |
| 12. #124×C83 | C4 | semidirect |
| 16. C2×C42×C83 | C4 | semidirect |
| 86. C83 | #2126 | semidirect |
| 91. C2×#41 | Dic83 | semidirect |
| 93. C4⋊Q8 | Dic83 | semidirect |
| 95. #124 | Dic83 | semidirect |
| 100. C2×C42 | Dic83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19127675 | 2 |
| #19127496 | 2 |
| #19127494 | 2 |
| #532×C83 | 2 |
| #2126 | 83 |