Finite Group DatabasebetaFinite Group DatabasebetaOrder 33536.
1284 conjugacy classes of subgroups; only the 242 normal subgroups are shown.
This group has 1284 conjugacy classes of subgroups — too many to draw. Only its 242 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 | C2×#120 |
| commutator, Frattini, cosocle | C24 | C24×C131 |
| prime radical | #3459×C131 | C2 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C131 ◁ C23×C4×C131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #2409×C131 | C2 | semidirect |
| 3. #2062×C131 | C2 | semidirect |
| 4. #2044×C131 | C2 | semidirect |
| 5. #1799×C131 | C2 | semidirect |
| 167. #29709 | C131 | direct (N × H) |
| 168. C131 | #29709 | direct (N × H) |
| 170. #2409 | C2×C131 | semidirect |
| 171. #2062 | C2×C131 | semidirect |
| 172. #2044 | C2×C131 | semidirect |
| 173. #1799 | C2×C131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3459×C131 | 2 |
| #2409×C131 | 2 |
| #2062×C131 | 2 |
| #2044×C131 | 2 |
| #1799×C131 | 2 |
| #29709 | 131 |