Finite Group DatabasebetaFinite Group DatabasebetaOrder 33536.
234 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 86 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 | #459 |
| commutator, Frattini, cosocle | C4×C8 | C23×C131 |
| prime radical | C2×D8×C131 | D4 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C131 ◁ C42×C131 ◁ C82×C131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #1713×C131 | C2 | semidirect |
| 4. #1370×C131 | C2 | semidirect |
| 5. #1365×C131 | C2 | semidirect |
| 39. D8×C131 | Q16 | semidirect |
| 86. #12447 | C131 | direct (N × H) |
| 87. C131 | #12447 | direct (N × H) |
| 89. #1713 | C2×C131 | semidirect |
| 91. #1370 | C2×C131 | semidirect |
| 92. #1365 | C2×C131 | semidirect |
| 126. D8 | Q16×C131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2226×C131 | 2 |
| #1713×C131 | 2 |
| C8×D8×C131 | 2 |
| #1370×C131 | 2 |
| #1365×C131 | 2 |
| #12447 | 131 |