Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
384 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#14581783 | C2 | semidirect |
| 3. #19128010 | C2 | semidirect |
| 4. #19128006 | C2 | semidirect |
| 5. #19128003 | C2 | semidirect |
| 6. #19127999 | C2 | semidirect |
| 7. #19127743 | C2 | semidirect |
| 8. #19127741 | C2 | semidirect |
| 9. #19127724 | C2 | semidirect |
| 136. C83 | #3080 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581783 | 2 |
| #41×Dic83 | 2 |
| #19128010 | 2 |
| #19128006 | 2 |
| #19128003 | 2 |
| #19127999 | 2 |
| #19127743 | 2 |
| #19127741 | 2 |
| #19127724 | 2 |
| #19127702 | 2 |
| #417×C83 | 2 |
| #3080 | 83 |