Finite Group DatabasebetaFinite Group DatabasebetaOrder 7232.
266 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 151 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×D113 |
| commutator | C2×C113 | C23×C4 |
| Frattini | C4 | C23×D113 |
| Fitting | C2×M16×C113 | C2 |
| socle | C22×C113 | C22×C4 |
| hypercenter | C2×M16 | D113 |
| hypocenter | C113 | C2×#131 |
| LCS | G ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C2×C4 ◁ C2×M16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16813630 | C2 | direct (N × H) |
| 3. C2×#14268630 | C2 | semidirect |
| 4. C22×#11744751 | C2 | semidirect |
| 5. C2×C8×D113 | C2 | semidirect |
| 6. C2×M16×C113 | C2 | semidirect |
| 13. #14268630 | C22 | semidirect |
| 16. C2×#11744751 | C22 | semidirect |
| 17. C8×D113 | C22 | semidirect |
| 19. M16×C113 | C22 | semidirect |
| 46. C2×C113 | #131 | semidirect |
| 49. C113 | C2×#131 | semidirect |
| 54. C2×M16 | D113 | semidirect |
| 65. M16 | C2×D113 | semidirect |
| 97. C2 | #16813630 | direct (N × H) |