Finite Group DatabasebetaFinite Group DatabasebetaOrder 7232.
202 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×#11744762 |
| commutator | C2×C113 | C22×C8 |
| Frattini | C2 | C22×#11744762 |
| Fitting | C23×C113 | C8 |
| socle | C22×C113 | C2×C8 |
| hypercenter | C23 | #11744762 |
| hypocenter | C113 | C2×C22⋊C8 |
| LCS | G ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C22 ◁ C23 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#11744762 | C2 | semidirect |
| 2. C22⋊#11744762 | C2 | direct (N × H) |
| 5. C2×#11744762 | C22 | semidirect |
| 12. C23×C113 | C8 | semidirect |
| 15. C22×D113 | C8 | semidirect |
| 16. C22×D113 | C8 | semidirect |
| 29. C22×C113 | C2×C8 | semidirect |
| 36. C2×D113 | C2×C8 | semidirect |
| 43. C2×C113 | C22⋊C8 | semidirect |
| 46. D113 | C22⋊C8 | semidirect |
| 49. C113 | C2×C22⋊C8 | semidirect |
| 68. C23 | #11744762 | semidirect |
| 88. C22 | C2×#11744762 | semidirect |
| 97. C2 | C22⋊#11744762 | direct (N × H) |