Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
520 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 157 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 |
|---|---|---|
| 2. #19127627 | C2 | semidirect |
| 3. #19127612 | C2 | semidirect |
| 4. #19127607 | C2 | semidirect |
| 6. #19127591 | C2 | semidirect |
| 7. C4×C4⋊Dic83 | C2 | semidirect |
| 8. C2×C4×Q8×C83 | C2 | semidirect |
| 102. C83 | #2592 | semidirect |
| 104. C2×C4×Q8 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581780 | 2 |
| #19127627 | 2 |
| #19127612 | 2 |
| #19127607 | 2 |
| #19127603 | 2 |
| #19127591 | 2 |
| C4×C4⋊Dic83 | 2 |
| C2×C4×Q8×C83 | 2 |
| #2592 | 83 |