Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
700 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 700 conjugacy classes of subgroups — too many to draw. Only its 216 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C269 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C269 |
| prime radical | C25×C269 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C269 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #397×C269 | C2 | semidirect |
| 3. #385×C269 | C2 | semidirect |
| 4. #381×C269 | C2 | semidirect |
| 9. C2×C4⋊C4×C269 | C22 | semidirect |
| 15. #95×C269 | C22 | semidirect |
| 16. #95×C269 | C22 | semidirect |
| 72. C269 | #2483 | direct (N × H) |
| 73. #2483 | C269 | direct (N × H) |
| 75. #397 | C2×C269 | semidirect |
| 76. #385 | C2×C269 | semidirect |
| 77. #381 | C2×C269 | semidirect |
| 82. C2×C4⋊C4 | C22×C269 | semidirect |
| 88. #95 | C22×C269 | semidirect |
| 89. #95 | C22×C269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊C4×C269 | 2 |
| #397×C269 | 2 |
| #385×C269 | 2 |
| #381×C269 | 2 |
| #379×C269 | 2 |
| #2483 | 269 |