Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
240 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C271 | C22⋊C4 |
| commutator | C2×C4 | C22×C4×C271 |
| Frattini, cosocle | C22×C4 | C23×C271 |
| socle | C22×C271 | C2×C22⋊C4 |
| prime radical | C23×C271 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C271 ◁ C2×C42×C271 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. C4⋊Q8×C271 | C4 | semidirect |
| 6. C4⋊Q8×C271 | C4 | semidirect |
| 11. C4×Q8×C271 | C4 | semidirect |
| 79. C271 | #1503 | direct (N × H) |
| 80. #1503 | C271 | direct (N × H) |
| 85. C4⋊Q8 | C4×C271 | semidirect |
| 86. C4⋊Q8 | C4×C271 | semidirect |
| 91. C4×Q8 | C4×C271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #533×C271 | 2 |
| #431×C271 | 2 |
| C4×C4⋊C4×C271 | 2 |
| #328×C271 | 2 |
| #1503 | 271 |