Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
404 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 139 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. #19128430 | C2 | semidirect |
| 2. #19128073 | C2 | semidirect |
| 3. #19127906 | C2 | semidirect |
| 4. #19127898 | C2 | semidirect |
| 5. Q8×C83⋊C8 | C2 | semidirect |
| 6. C4×#13050578 | C2 | semidirect |
| 45. Q8×C83 | SD16 | semidirect |
| 60. C83⋊C8 | #41 | semidirect |
| 77. C83 | #3392 | semidirect |
| 124. Q8 | #13050578 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128430 | 2 |
| #19128073 | 2 |
| #19127906 | 2 |
| #19127898 | 2 |
| Q8×C83⋊C8 | 2 |
| C4×#13050578 | 2 |
| #550×C83 | 2 |
| #3392 | 83 |