Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
176 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 63 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. #19127778 | C2 | semidirect |
| 3. #19127428 | C2 | semidirect |
| 4. #19127422 | C2 | semidirect |
| 5. #334×C83 | C2 | semidirect |
| 39. C8×C83 | M16 | semidirect |
| 56. C83 | #1594 | semidirect |
| 59. #334 | D83 | semidirect |
| 97. C8 | #13050573 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D664 | 2 |
| #19127778 | 2 |
| #19127428 | 2 |
| #19127422 | 2 |
| #334×C83 | 2 |
| #1594 | 83 |