Finite Group DatabasebetaFinite Group DatabasebetaOrder 7232.
258 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 103 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×Q8×D113 | C2 | semidirect |
| 3. #16813654 | C2 | direct (N × H) |
| 4. C2×#14268637 | C2 | semidirect |
| 5. C2×#14268636 | C2 | semidirect |
| 6. C2×#14268634 | C2 | semidirect |
| 7. C2×#14268630 | C2 | semidirect |
| 8. C2×Q16×C113 | C2 | semidirect |
| 14. Q8×D113 | C22 | semidirect |
| 20. #14268637 | C22 | semidirect |
| 21. #14268636 | C22 | semidirect |
| 22. #14268634 | C22 | semidirect |
| 23. #14268630 | C22 | semidirect |
| 27. Q16×C113 | C22 | semidirect |
| 63. C2×C113 | #137 | semidirect |
| 67. C113 | C2×#137 | semidirect |
| 73. C2×Q16 | D113 | semidirect |
| 91. Q16 | C2×D113 | semidirect |
| 133. C2 | #16813654 | direct (N × H) |