Finite Group DatabasebetaFinite Group DatabasebetaOrder 7232.
198 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 45 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. C2×D4×D113 | C2 | semidirect |
| 2. C2×#14268632 | C2 | semidirect |
| 3. #16813593 | C2 | semidirect |
| 4. #16813544 | C2 | semidirect |
| 5. #16813543 | C2 | semidirect |
| 6. #16813534 | C2 | semidirect |
| 7. C2×D8×C113 | C2 | semidirect |
| 16. C2×#11744751 | C22 | semidirect |
| 17. C4⋊Dic113 | C22 | semidirect |
| 20. C2×D4×C113 | C22 | semidirect |
| 22. C2×C8×C113 | C22 | semidirect |
| 33. D4×C113 | D4 | semidirect |
| 40. D452 | D4 | semidirect |
| 58. C2×D113 | D8 | semidirect |
| 70. C113 | #447 | semidirect |
| 74. C2×D8 | D113 | semidirect |
| 86. C2×D4 | C2×D113 | semidirect |
| 91. C2×C8 | C2×D113 | semidirect |
| 108. D4 | C22⋊D113 | semidirect |