Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
174 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 116 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C16×C271 | C22 |
| commutator | C2 | C22×C16×C271 |
| Frattini, cosocle | C2×C8 | C23×C271 |
| socle | C22×C271 | C22×C8 |
| prime radical | C2×D4×C271 | C8 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C16×C271 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C16×C271 | C2 | semidirect |
| 3. C4⋊C16×C271 | C2 | semidirect |
| 4. C22⋊C16×C271 | C2 | semidirect |
| 5. C4×C16×C271 | C2 | semidirect |
| 27. C16×C271 | D4 | direct (N × H) |
| 29. D4×C271 | C16 | direct (N × H) |
| 42. C22×C271 | C2×C16 | semidirect |
| 46. C4×C271 | C2×C16 | semidirect |
| 53. C271 | D4×C16 | direct (N × H) |
| 54. D4×C16 | C271 | direct (N × H) |
| 55. C22×C16 | C2×C271 | semidirect |
| 57. C4⋊C16 | C2×C271 | semidirect |
| 58. C22⋊C16 | C2×C271 | semidirect |
| 59. C4×C16 | C2×C271 | semidirect |
| 81. C16 | D4×C271 | direct (N × H) |
| 83. D4 | C16×C271 | direct (N × H) |
| 96. C22 | C2×C16×C271 | semidirect |
| 100. C4 | C2×C16×C271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C16×C271 | 2 |
| C8×D4×C271 | 2 |
| C4⋊C16×C271 | 2 |
| C22⋊C16×C271 | 2 |
| C4×C16×C271 | 2 |
| D4×C16 | 271 |