Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
348 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 69 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. C2×#14581822 | C2 | semidirect |
| 3. #19128277 | C2 | semidirect |
| 4. #19127719 | C2 | semidirect |
| 5. #19127709 | C2 | semidirect |
| 6. #19127471 | C2 | semidirect |
| 7. #410×C83 | C2 | semidirect |
| 137. C83 | #2009 | semidirect |
| 143. #410 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128499 | 2 |
| C2×#14581822 | 2 |
| #19128277 | 2 |
| #19127719 | 2 |
| #19127709 | 2 |
| #19127471 | 2 |
| #410×C83 | 2 |
| #2009 | 83 |