Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
612 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 136 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C271 | C2×C22⋊C4 |
| commutator | C23 | C22×C4×C271 |
| Frattini, cosocle | C24 | C23×C271 |
| prime radical | C22×#41×C271 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C271 ◁ C23×C4×C271 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#99×C271 | C2 | semidirect |
| 3. #381×C271 | C2 | semidirect |
| 6. C22×Q8×C271 | C4 | semidirect |
| 7. C22×D4×C271 | C4 | semidirect |
| 9. C23×C4×C271 | C4 | semidirect |
| 75. C271 | #1782 | direct (N × H) |
| 76. #1782 | C271 | direct (N × H) |
| 78. C2×#99 | C2×C271 | semidirect |
| 79. #381 | C2×C271 | semidirect |
| 82. C22×Q8 | C4×C271 | semidirect |
| 83. C22×D4 | C4×C271 | semidirect |
| 85. C23×C4 | C4×C271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#41×C271 | 2 |
| C2×#99×C271 | 2 |
| #381×C271 | 2 |
| #1782 | 271 |