Finite Group DatabasebetaFinite Group DatabasebetaOrder 33536.
408 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 74 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, Frattini, cosocle | C2×C4⋊C4 | C23×C131 |
| prime radical | #537×C131 | C22 |
| LCS | G ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C131 ◁ C23×C131 ◁ C2×C4⋊C4×C131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #2799×C131 | C2 | semidirect |
| 5. #1354×C131 | C2 | semidirect |
| 6. #1353×C131 | C2 | semidirect |
| 7. #1319×C131 | C2 | semidirect |
| 75. C2×Q8×C131 | SD16 | semidirect |
| 180. #12128 | C131 | direct (N × H) |
| 181. C131 | #12128 | direct (N × H) |
| 182. #2799 | C2×C131 | semidirect |
| 186. #1354 | C2×C131 | semidirect |
| 187. #1353 | C2×C131 | semidirect |
| 188. #1319 | C2×C131 | semidirect |
| 256. C2×Q8 | SD16×C131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2799×C131 | 2 |
| #2007×C131 | 2 |
| #1616×C131 | 2 |
| #1604×C131 | 2 |
| #1354×C131 | 2 |
| #1353×C131 | 2 |
| #1319×C131 | 2 |
| #12128 | 131 |