Finite Group DatabasebetaFinite Group DatabasebetaOrder 33536.
304 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C131 | #1505 |
| commutator | C2×C8 | C22×C4×C131 |
| Frattini, cosocle | C2×M16 | C23×C131 |
| prime radical | #469×C131 | C22 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C131 ◁ C2×C4×C131 ◁ #405×C131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #2166×C131 | C2 | semidirect |
| 3. #1747×C131 | C2 | semidirect |
| 4. #1342×C131 | C2 | semidirect |
| 6. #1340×C131 | C2 | semidirect |
| 9. #498×C131 | C4 | semidirect |
| 10. #495×C131 | C4 | semidirect |
| 15. #442×C131 | C4 | semidirect |
| 16. #441×C131 | C4 | semidirect |
| 144. #11769 | C131 | direct (N × H) |
| 145. C131 | #11769 | direct (N × H) |
| 147. #2166 | C2×C131 | semidirect |
| 148. #1747 | C2×C131 | semidirect |
| 149. #1342 | C2×C131 | semidirect |
| 151. #1340 | C2×C131 | semidirect |
| 154. #498 | C4×C131 | semidirect |
| 155. #495 | C4×C131 | semidirect |
| 160. #442 | C4×C131 | semidirect |
| 161. #441 | C4×C131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3173×C131 | 2 |
| #2166×C131 | 2 |
| #1747×C131 | 2 |
| #1342×C131 | 2 |
| #1341×C131 | 2 |
| #1340×C131 | 2 |
| #1339×C131 | 2 |
| #11769 | 131 |