Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
402 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 3. C2×#14581715 | C2 | semidirect |
| 5. #19127606 | C2 | semidirect |
| 6. #19127455 | C2 | semidirect |
| 7. #340×C83 | C2 | semidirect |
| 13. C2×#13050579 | C4 | semidirect |
| 32. C2×Dic166 | C2×C4 | semidirect |
| 57. C2×C8×C83 | C2×C4 | semidirect |
| 90. C2×Dic83 | SD16 | semidirect |
| 134. C83 | #1877 | semidirect |
| 140. #340 | D83 | semidirect |
| 188. C2×C8 | C4×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13050579 | 2 |
| C2×#14581754 | 2 |
| C2×#14581715 | 2 |
| C2×#14581712 | 2 |
| #19127606 | 2 |
| #19127455 | 2 |
| #340×C83 | 2 |
| #1877 | 83 |