Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
220 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 68 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 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C23×C269 |
| prime radical | C2×#135×C269 | C2 |
| LCS | G ▷ C2×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 |
|---|---|---|
| 2. C2×Q32×C269 | C2 | semidirect |
| 3. C2×SD32×C269 | C2 | semidirect |
| 4. #467×C269 | C2 | semidirect |
| 5. #358×C269 | C2 | semidirect |
| 6. #357×C269 | C2 | semidirect |
| 7. C22⋊C16×C269 | C2 | semidirect |
| 85. C269 | #2189 | direct (N × H) |
| 86. #2189 | C269 | direct (N × H) |
| 88. C2×Q32 | C2×C269 | semidirect |
| 89. C2×SD32 | C2×C269 | semidirect |
| 90. #467 | C2×C269 | semidirect |
| 91. #358 | C2×C269 | semidirect |
| 92. #357 | C2×C269 | semidirect |
| 93. C22⋊C16 | C2×C269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#135×C269 | 2 |
| C2×Q32×C269 | 2 |
| C2×SD32×C269 | 2 |
| #467×C269 | 2 |
| #358×C269 | 2 |
| #357×C269 | 2 |
| C22⋊C16×C269 | 2 |
| #2189 | 269 |