Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
152 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 104 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C269 | #106 |
| commutator | C8 | C22×C4×C269 |
| Frattini, cosocle | C2×C8 | C23×C269 |
| prime radical | C23×C269 | SD16 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C269 ◁ C22×C4×C269 ◁ C22×C8×C269 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #365×C269 | C2 | direct (N × H) |
| 8. M32×C269 | C4 | semidirect |
| 10. C2×C16×C269 | C4 | semidirect |
| 28. C16×C269 | C2×C4 | semidirect |
| 54. C2×C269 | #365 | direct (N × H) |
| 56. C269 | C2×#365 | direct (N × H) |
| 57. C2×#365 | C269 | direct (N × H) |
| 61. #365 | C2×C269 | direct (N × H) |
| 65. M32 | C4×C269 | semidirect |
| 67. C2×C16 | C4×C269 | semidirect |
| 85. C16 | C2×C4×C269 | semidirect |
| 111. C2 | #365×C269 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M32×C269 | 2 |
| C2×#108×C269 | 2 |
| C2×#106×C269 | 2 |
| #365×C269 | 2 |
| C2×#365 | 269 |