Finite Group DatabasebetaFinite Group DatabasebetaOrder 33664.
890 conjugacy classes of subgroups.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C263 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C263 |
| prime radical | C23×C263 | C24 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C263 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #564×C263 | C2 | semidirect |
| 2. #557×C263 | C2 | semidirect |
| 40. C263 | #3556 | direct (N × H) |
| 41. #3556 | C263 | direct (N × H) |
| 42. #564 | C2×C263 | semidirect |
| 43. #557 | C2×C263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #564×C263 | 2 |
| #557×C263 | 2 |
| #541×C263 | 2 |
| #533×C263 | 2 |
| #3556 | 263 |