Finite Group DatabasebetaFinite Group DatabasebetaOrder 33536.
308 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 308 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 | #2206×C131 | C2 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C131 ◁ C42×C131 ◁ #446×C131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #3389×C131 | C2 | semidirect |
| 2. #2244×C131 | C2 | semidirect |
| 4. #1688×C131 | C2 | semidirect |
| 5. #1363×C131 | C2 | semidirect |
| 6. #1338×C131 | C2 | semidirect |
| 7. #1333×C131 | C2 | semidirect |
| 75. D8×C131 | SD16 | semidirect |
| 145. #12360 | C131 | direct (N × H) |
| 146. C131 | #12360 | direct (N × H) |
| 147. #3389 | C2×C131 | semidirect |
| 148. #2244 | C2×C131 | semidirect |
| 150. #1688 | C2×C131 | semidirect |
| 151. #1363 | C2×C131 | semidirect |
| 152. #1338 | C2×C131 | semidirect |
| 153. #1333 | C2×C131 | semidirect |
| 221. D8 | SD16×C131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3389×C131 | 2 |
| #2244×C131 | 2 |
| #2206×C131 | 2 |
| #1688×C131 | 2 |
| #1363×C131 | 2 |
| #1338×C131 | 2 |
| #1333×C131 | 2 |
| #12360 | 131 |