Finite Group DatabasebetaFinite Group DatabasebetaOrder 33536.
278 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 74 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 | #2184 |
| commutator, Frattini, cosocle | C2×C16 | C23×C131 |
| LCS | G ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C131 ◁ C2×C4×C131 ◁ #131×C131 ◁ #504×C131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #3417×C131 | C2 | semidirect |
| 2. #2263×C131 | C2 | semidirect |
| 3. C2×SD64×C131 | C2 | semidirect |
| 4. #2221×C131 | C2 | semidirect |
| 5. #1420×C131 | C2 | semidirect |
| 6. #1417×C131 | C2 | semidirect |
| 7. #1401×C131 | C2 | semidirect |
| 118. #13670 | C131 | direct (N × H) |
| 119. C131 | #13670 | direct (N × H) |
| 120. #3417 | C2×C131 | semidirect |
| 121. #2263 | C2×C131 | semidirect |
| 122. C2×SD64 | C2×C131 | semidirect |
| 123. #2221 | C2×C131 | semidirect |
| 124. #1420 | C2×C131 | semidirect |
| 125. #1417 | C2×C131 | semidirect |
| 126. #1401 | C2×C131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3417×C131 | 2 |
| #2263×C131 | 2 |
| C2×SD64×C131 | 2 |
| #2221×C131 | 2 |
| #1420×C131 | 2 |
| #1417×C131 | 2 |
| #1401×C131 | 2 |
| #13670 | 131 |