Finite Group DatabasebetaFinite Group DatabasebetaOrder 33536.
656 conjugacy classes of subgroups; only the 238 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 238 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C131 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C131 |
| prime radical | C22×D4×C131 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C131 ◁ #376×C131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #2645×C131 | C2 | semidirect |
| 4. #1941×C131 | C2 | semidirect |
| 6. #1935×C131 | C2 | semidirect |
| 7. #1726×C131 | C2 | semidirect |
| 115. #33271 | C131 | direct (N × H) |
| 116. C131 | #33271 | direct (N × H) |
| 117. #2645 | C2×C131 | semidirect |
| 120. #1941 | C2×C131 | semidirect |
| 122. #1935 | C2×C131 | semidirect |
| 123. #1726 | C2×C131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2645×C131 | 2 |
| #2644×C131 | 2 |
| #1968×C131 | 2 |
| #1941×C131 | 2 |
| #1936×C131 | 2 |
| #1935×C131 | 2 |
| #1726×C131 | 2 |
| #33271 | 131 |