Finite Group DatabasebetaFinite Group DatabasebetaOrder 33536.
368 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 90 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 | #99 |
| commutator | C22×C4 | C2×C8×C131 |
| Frattini, cosocle | C2×#95 | C22×C131 |
| prime radical | C24×C131 | C22⋊C4 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C131 ◁ C24×C131 ◁ C2×#95×C131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 29. #95×C131 | C8 | semidirect |
| 161. #7122 | C131 | direct (N × H) |
| 162. C131 | #7122 | direct (N × H) |
| 191. #95 | C8×C131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #1442×C131 | 2 |
| #1280×C131 | 2 |
| #7122 | 131 |