Finite Group DatabasebetaFinite Group DatabasebetaOrder 33536.
120 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C16×C131 | D8 |
| commutator | C8 | C2×C16×C131 |
| Frattini, cosocle | C4×C16 | C22×C131 |
| socle | C2×C131 | D4⋊C16 |
| prime radical | #135×C131 | C8 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C16×C131 ◁ C2×C16×C131 ◁ C4×C16×C131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #1422×C131 | C2 | semidirect |
| 3. C4×C32×C131 | C2 | semidirect |
| 57. #7381 | C131 | direct (N × H) |
| 58. C131 | #7381 | direct (N × H) |
| 60. #1422 | C2×C131 | semidirect |
| 61. C4×C32 | C2×C131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2170×C131 | 2 |
| #1422×C131 | 2 |
| C4×C32×C131 | 2 |
| #7381 | 131 |