Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
134 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C269 | #481 |
| commutator, Frattini, cosocle | C2×C8 | C23×C269 |
| prime radical | #469×C269 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C269 ◁ C2×C4×C269 ◁ C2×M16×C269 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #430×C269 | C2 | semidirect |
| 3. #365×C269 | C2 | semidirect |
| 4. #361×C269 | C2 | semidirect |
| 5. #349×C269 | C2 | semidirect |
| 55. C269 | #2238 | direct (N × H) |
| 56. #2238 | C269 | direct (N × H) |
| 58. #430 | C2×C269 | semidirect |
| 59. #365 | C2×C269 | semidirect |
| 60. #361 | C2×C269 | semidirect |
| 61. #349 | C2×C269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #469×C269 | 2 |
| #430×C269 | 2 |
| #365×C269 | 2 |
| #361×C269 | 2 |
| #349×C269 | 2 |
| #2238 | 269 |