Finite Group DatabasebetaFinite Group DatabasebetaOrder 33536.
428 conjugacy classes of subgroups; only the 182 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 182 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C42×C131 | C2×D4 |
| commutator | C2×C4 | C2×C42×C131 |
| Frattini, cosocle | C2×C42 | C23×C131 |
| socle | C22×C131 | C4×C22⋊C4 |
| prime radical | C2×#41×C131 | C2×C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C42×C131 ◁ C2×C4×C8×C131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #1452×C131 | C2 | semidirect |
| 4. C2×C82×C131 | C2 | semidirect |
| 5. #1278×C131 | C2 | semidirect |
| 99. #8187 | C131 | direct (N × H) |
| 100. C131 | #8187 | direct (N × H) |
| 103. #1452 | C2×C131 | semidirect |
| 104. C2×C82 | C2×C131 | semidirect |
| 105. #1278 | C2×C131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2922×C131 | 2 |
| #1476×C131 | 2 |
| #1452×C131 | 2 |
| C2×C82×C131 | 2 |
| #1278×C131 | 2 |
| #8187 | 131 |