Finite Group DatabasebetaFinite Group DatabasebetaOrder 7232.
266 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C8 | C22×D113 |
| commutator, socle | C2×C113 | C23×C4 |
| Frattini | C4 | C23×D113 |
| Fitting | #131×C113 | C2 |
| hypercenter | #131 | D113 |
| hypocenter | C113 | C2×#131 |
| LCS | G ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C8 ◁ #131 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16813630 | C2 | semidirect |
| 3. #16813629 | C2 | semidirect |
| 4. #16813628 | C2 | semidirect |
| 5. M16×D113 | C2 | semidirect |
| 6. C2×C8×D113 | C2 | semidirect |
| 7. #131×C113 | C2 | semidirect |
| 14. #14268631 | C22 | semidirect |
| 15. #14268630 | C22 | semidirect |
| 16. C2×#11744751 | C22 | semidirect |
| 19. C8×D113 | C22 | semidirect |
| 20. C8×D113 | C22 | semidirect |
| 22. M16×C113 | C22 | semidirect |
| 23. C2×C8×C113 | C22 | semidirect |
| 51. D113 | #131 | direct (N × H) |
| 52. C113 | C2×#131 | semidirect |
| 58. #131 | D113 | direct (N × H) |
| 70. M16 | C2×D113 | semidirect |
| 76. C2×C8 | C2×D113 | semidirect |