Finite Group DatabasebetaFinite Group DatabasebetaOrder 33536.
398 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 90 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 | #393 |
| commutator, Frattini, cosocle | C2×C42 | C23×C131 |
| prime radical | #532×C131 | C22 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C131 ◁ C2×C42×C131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #2605×C131 | C2 | semidirect |
| 5. #1300×C131 | C2 | semidirect |
| 6. #1288×C131 | C2 | semidirect |
| 7. #1285×C131 | C2 | semidirect |
| 30. C4⋊Q8×C131 | Q8 | semidirect |
| 31. #127×C131 | Q8 | semidirect |
| 181. #10378 | C131 | direct (N × H) |
| 182. C131 | #10378 | direct (N × H) |
| 183. #2605 | C2×C131 | semidirect |
| 187. #1300 | C2×C131 | semidirect |
| 188. #1288 | C2×C131 | semidirect |
| 189. #1285 | C2×C131 | semidirect |
| 212. C4⋊Q8 | Q8×C131 | semidirect |
| 213. #127 | Q8×C131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2605×C131 | 2 |
| #1980×C131 | 2 |
| #1514×C131 | 2 |
| #1505×C131 | 2 |
| #1300×C131 | 2 |
| #1288×C131 | 2 |
| #1285×C131 | 2 |
| #10378 | 131 |