Finite Group DatabasebetaFinite Group DatabasebetaOrder 7232.
426 conjugacy classes of subgroups; only the 215 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 215 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D113 |
| commutator | C2×C113 | C23×C4 |
| Frattini | C22 | C23×D113 |
| Fitting | C22×D4×C113 | C2 |
| socle | C23×C113 | C23 |
| hypercenter | C22×D4 | D113 |
| hypocenter | C113 | C2×C4×D4 |
| LCS | G ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C23 ◁ C22×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×Dic113 | C2 | semidirect |
| 2. D4×Dic113 | C2 | direct (N × H) |
| 3. C2×C4⋊Dic113 | C2 | semidirect |
| 4. C2×C22⋊Dic113 | C2 | semidirect |
| 5. C2×C4×Dic113 | C2 | semidirect |
| 11. C22×Dic113 | C22 | semidirect |
| 12. C4⋊Dic113 | C22 | semidirect |
| 13. C22⋊Dic113 | C22 | semidirect |
| 14. C4×Dic113 | C22 | semidirect |
| 16. C2×D4×C113 | C4 | semidirect |
| 21. C23×C113 | C2×C4 | semidirect |
| 24. D4×C113 | C2×C4 | semidirect |
| 25. C2×C4×C113 | C2×C4 | semidirect |
| 30. C2×Dic113 | D4 | direct (N × H) |
| 38. C22×C113 | C22×C4 | semidirect |
| 42. C4×C113 | C22×C4 | semidirect |
| 45. Dic113 | C2×D4 | direct (N × H) |
| 47. C2×C113 | C4×D4 | semidirect |
| 51. C113 | C2×C4×D4 | semidirect |
| 60. C2×D4 | Dic113 | direct (N × H) |
| 73. C23 | C2×Dic113 | semidirect |
| 76. D4 | C2×Dic113 | direct (N × H) |
| 84. C2×C4 | C2×Dic113 | semidirect |
| 90. C22 | C22×Dic113 | semidirect |
| 97. C4 | C22×Dic113 | semidirect |
| 99. C2 | D4×Dic113 | direct (N × H) |