Finite Group DatabasebetaFinite Group DatabasebetaOrder 10112.
544 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 173 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 |
|---|---|---|
| 3. #19098765 | C2 | direct (N × H) |
| 4. C2×C4⋊(C79⋊C8) | C2 | semidirect |
| 5. C2×#14579085 | C2 | semidirect |
| 6. C2×C4⋊Q8×C79 | C2 | semidirect |
| 16. C4⋊(C79⋊C8) | C22 | semidirect |
| 17. #14579085 | C22 | semidirect |
| 20. C4⋊Q8×C79 | C22 | semidirect |
| 61. C2×C4×C79 | SD16 | semidirect |
| 86. C4×C79 | C2×SD16 | semidirect |
| 90. C2×C79 | #461 | semidirect |
| 96. C79 | C2×#461 | semidirect |
| 98. C2×C4⋊Q8 | D79 | semidirect |
| 110. C4⋊Q8 | C2×D79 | semidirect |
| 163. C2×C4 | #11929611 | semidirect |
| 183. C4 | C2×#11929611 | semidirect |
| 187. C2 | #19098765 | direct (N × H) |