Finite Group DatabasebetaFinite Group DatabasebetaOrder 33536.
424 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 424 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 | C22×C131 | #447 |
| commutator, Frattini, cosocle | C4×C8 | C23×C131 |
| prime radical | D4×D8×C131 | C2 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C131 ◁ C42×C131 ◁ C8×D4×C131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #2240×C131 | C2 | semidirect |
| 3. #2224×C131 | C2 | semidirect |
| 4. #1673×C131 | C2 | semidirect |
| 5. #1361×C131 | C2 | semidirect |
| 6. #1331×C131 | C2 | semidirect |
| 7. D4⋊C16×C131 | C2 | semidirect |
| 10. #500×C131 | C22 | semidirect |
| 19. C4⋊C16×C131 | C22 | semidirect |
| 22. C4×C16×C131 | C22 | semidirect |
| 23. #335×C131 | C22 | semidirect |
| 75. D8×C131 | SD16 | semidirect |
| 151. #12368 | C131 | direct (N × H) |
| 152. C131 | #12368 | direct (N × H) |
| 154. #2240 | C2×C131 | semidirect |
| 155. #2224 | C2×C131 | semidirect |
| 156. #1673 | C2×C131 | semidirect |
| 157. #1361 | C2×C131 | semidirect |
| 158. #1331 | C2×C131 | semidirect |
| 159. D4⋊C16 | C2×C131 | semidirect |
| 162. #500 | C22×C131 | semidirect |
| 171. C4⋊C16 | C22×C131 | semidirect |
| 174. C4×C16 | C22×C131 | semidirect |
| 175. #335 | C22×C131 | semidirect |
| 227. D8 | SD16×C131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D8×C131 | 2 |
| #2240×C131 | 2 |
| #2224×C131 | 2 |
| #1673×C131 | 2 |
| #1361×C131 | 2 |
| #1331×C131 | 2 |
| D4⋊C16×C131 | 2 |
| #12368 | 131 |