Finite Group DatabasebetaFinite Group DatabasebetaOrder 7232.
134 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C8 | C2×D113 |
| commutator | C2×C113 | C22×C8 |
| Frattini | C2×C4 | C22×D113 |
| Fitting | C22×C8×C113 | C2 |
| socle | C22×C113 | C22×C4 |
| hypercenter | C22×C8 | D113 |
| hypocenter | C113 | C8×D4 |
| LCS | G ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C2×C8 ◁ C22×C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C8×D113 | C2 | semidirect |
| 3. #16813551 | C2 | semidirect |
| 4. C22⋊#11744751 | C2 | semidirect |
| 5. #16813534 | C2 | semidirect |
| 6. C8×Dic113 | C2 | semidirect |
| 7. C22×C8×C113 | C2 | semidirect |
| 27. C22⋊D113 | C8 | direct (N × H) |
| 34. C8×C113 | D4 | semidirect |
| 39. C22×C113 | C2×C8 | semidirect |
| 43. C2×D113 | C2×C8 | semidirect |
| 49. Dic113 | C2×C8 | semidirect |
| 55. C113 | C8×D4 | semidirect |
| 58. C22×C8 | D113 | semidirect |
| 92. C8 | C22⋊D113 | direct (N × H) |
| 98. C22 | C8×D113 | semidirect |