Finite Group DatabasebetaFinite Group DatabasebetaOrder 33536.
342 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 122 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 | C2×D8 |
| commutator, Frattini, cosocle | C22×C8 | C23×C131 |
| prime radical | C24×C131 | D8 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C131 ◁ C23×C4×C131 ◁ C23×C8×C131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#366×C131 | C2 | semidirect |
| 4. #1380×C131 | C2 | semidirect |
| 5. #1380×C131 | C2 | semidirect |
| 106. #13492 | C131 | direct (N × H) |
| 107. C131 | #13492 | direct (N × H) |
| 108. C2×#366 | C2×C131 | semidirect |
| 111. #1380 | C2×C131 | semidirect |
| 112. #1380 | C2×C131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#366×C131 | 2 |
| C2×C22⋊C16×C131 | 2 |
| #1808×C131 | 2 |
| #1380×C131 | 2 |
| #13492 | 131 |