Finite Group DatabasebetaFinite Group DatabasebetaOrder 33536.
306 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 82 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×C131 | #447 |
| commutator, Frattini, cosocle | C4×C8 | C23×C131 |
| prime radical | #493×C131 | C22 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C131 ◁ C42×C131 ◁ C8×Q8×C131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #2225×C131 | C2 | semidirect |
| 4. #1674×C131 | C2 | semidirect |
| 6. Q8⋊C16×C131 | C2 | semidirect |
| 7. #1332×C131 | C2 | semidirect |
| 128. #12381 | C131 | direct (N × H) |
| 129. C131 | #12381 | direct (N × H) |
| 132. #2225 | C2×C131 | semidirect |
| 133. #1674 | C2×C131 | semidirect |
| 135. Q8⋊C16 | C2×C131 | semidirect |
| 136. #1332 | C2×C131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3396×C131 | 2 |
| #2240×C131 | 2 |
| #2225×C131 | 2 |
| #1674×C131 | 2 |
| #1361×C131 | 2 |
| Q8⋊C16×C131 | 2 |
| #1332×C131 | 2 |
| #12381 | 131 |