Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
360 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 144 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×C271 | C2×D4 |
| commutator | C2×C4 | C22×C4×C271 |
| Frattini, cosocle | C22×C4 | C23×C271 |
| prime radical | C24×C271 | D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C271 ◁ C23×C4×C271 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#107×C271 | C2 | semidirect |
| 5. #340×C271 | C2 | semidirect |
| 16. C22⋊C8×C271 | C4 | semidirect |
| 33. C2×C8×C271 | C2×C4 | semidirect |
| 74. C22×C271 | #107 | semidirect |
| 96. C271 | #1852 | direct (N × H) |
| 97. #1852 | C271 | direct (N × H) |
| 99. C2×#107 | C2×C271 | semidirect |
| 102. #340 | C2×C271 | semidirect |
| 113. C22⋊C8 | C4×C271 | semidirect |
| 130. C2×C8 | C2×C4×C271 | semidirect |
| 171. C22 | #107×C271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊C4×C271 | 2 |
| C2×#107×C271 | 2 |
| C2×C22⋊C8×C271 | 2 |
| #380×C271 | 2 |
| #340×C271 | 2 |
| #1852 | 271 |