Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
548 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 132 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C269 | #120 |
| commutator | C2×C4 | C22×C4×C269 |
| Frattini, cosocle | C22×C4 | C23×C269 |
| socle | C2×C269 | #379 |
| prime radical | #585×C269 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C269 ◁ C22×C4×C269 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #421×C269 | C2 | semidirect |
| 3. #416×C269 | C2 | semidirect |
| 4. #410×C269 | C2 | semidirect |
| 5. #408×C269 | C2 | semidirect |
| 7. 2−1+4×C269 | C4 | semidirect |
| 10. H(5,𝔽2)×C269 | C4 | semidirect |
| 15. C2×M16×C269 | C22 | semidirect |
| 16. C22×C8×C269 | C22 | semidirect |
| 17. #117×C269 | C22 | semidirect |
| 108. C269 | #1794 | direct (N × H) |
| 109. #1794 | C269 | direct (N × H) |
| 111. #421 | C2×C269 | semidirect |
| 112. #416 | C2×C269 | semidirect |
| 113. #410 | C2×C269 | semidirect |
| 114. #408 | C2×C269 | semidirect |
| 116. 2−1+4 | C4×C269 | semidirect |
| 119. H(5,𝔽2) | C4×C269 | semidirect |
| 124. C2×M16 | C22×C269 | semidirect |
| 125. C22×C8 | C22×C269 | semidirect |
| 126. #117 | C22×C269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #585×C269 | 2 |
| #421×C269 | 2 |
| #416×C269 | 2 |
| #410×C269 | 2 |
| #408×C269 | 2 |
| #1794 | 269 |