Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
144 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 45 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×#14581737 | C2 | semidirect |
| 2. #19128117 | C2 | semidirect |
| 3. #19127977 | C2 | semidirect |
| 5. #19127516 | C2 | semidirect |
| 6. #19127513 | C2 | semidirect |
| 7. #368×C83 | C2 | semidirect |
| 72. C83 | #2223 | semidirect |
| 77. #368 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581737 | 2 |
| #19128117 | 2 |
| #19127977 | 2 |
| #19127972 | 2 |
| #19127516 | 2 |
| #19127513 | 2 |
| #368×C83 | 2 |
| #2223 | 83 |