Finite Group DatabasebetaFinite Group DatabasebetaOrder 33536.
932 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 932 conjugacy classes of subgroups — too many to draw. Only its 142 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 | B(4,𝔽2) |
| commutator | C2×Q8 | C22×C4×C131 |
| Frattini, cosocle | C22×Q8 | C23×C131 |
| prime radical | C2×H(3,𝔽4)×C131 | C2 |
| LCS | G ▷ C2×Q8 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C131 ◁ C23×C131 ◁ C22×Q8×C131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#355×C131 | C2 | semidirect |
| 3. #1888×C131 | C2 | semidirect |
| 5. H(3,𝔽4)×C131 | C4 | semidirect |
| 9. #519×C131 | C22 | semidirect |
| 11. C2×#101×C131 | C22 | semidirect |
| 105. #12774 | C131 | direct (N × H) |
| 106. C131 | #12774 | direct (N × H) |
| 108. C2×#355 | C2×C131 | semidirect |
| 109. #1888 | C2×C131 | semidirect |
| 111. H(3,𝔽4) | C4×C131 | semidirect |
| 115. #519 | C22×C131 | semidirect |
| 117. C2×#101 | C22×C131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×H(3,𝔽4)×C131 | 2 |
| C2×#355×C131 | 2 |
| #1888×C131 | 2 |
| #12774 | 131 |