Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
266 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 73 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. #19127723 | C2 | semidirect |
| 3. C4×#13050573 | C2 | semidirect |
| 4. Q8⋊(C83⋊C8) | C2 | semidirect |
| 5. #19127430 | C2 | semidirect |
| 6. #19127428 | C2 | semidirect |
| 7. Q8⋊C8×C83 | C2 | semidirect |
| 61. Q8×C83 | M16 | semidirect |
| 73. D332 | M16 | semidirect |
| 111. C83 | #1489 | semidirect |
| 116. Q8⋊C8 | D83 | semidirect |
| 172. Q8 | #13050573 | semidirect |