Finite Group DatabasebetaFinite Group DatabasebetaOrder 33536.
686 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 686 conjugacy classes of subgroups — too many to draw. Only its 142 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×#99 |
| commutator | C2×C4 | C22×C8×C131 |
| Frattini, cosocle | C2×C4⋊C4 | C23×C131 |
| prime radical | C23×D4×C131 | C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C131 ◁ C22×C4×C131 ◁ C2×#117×C131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #1458×C131 | C2 | semidirect |
| 3. #1318×C131 | C2 | semidirect |
| 12. #324×C131 | C22 | semidirect |
| 19. C22×D4×C131 | C8 | semidirect |
| 137. #11433 | C131 | direct (N × H) |
| 138. C131 | #11433 | direct (N × H) |
| 140. #1458 | C2×C131 | semidirect |
| 141. #1318 | C2×C131 | semidirect |
| 150. #324 | C22×C131 | semidirect |
| 157. C22×D4 | C8×C131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2309×C131 | 2 |
| #1458×C131 | 2 |
| #1318×C131 | 2 |
| #11433 | 131 |