Finite Group DatabasebetaFinite Group DatabasebetaOrder 33536.
284 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 110 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 | #493 |
| commutator, Frattini, cosocle | C4×C8 | C23×C131 |
| prime radical | #493×C131 | C22 |
| 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 |
|---|---|---|
| 1. #2254×C131 | C2 | semidirect |
| 3. #2241×C131 | C2 | semidirect |
| 5. #1707×C131 | C2 | semidirect |
| 7. C8×C16×C131 | C2 | semidirect |
| 68. C16×C131 | SD16 | semidirect |
| 85. C8×C131 | SD32 | semidirect |
| 103. #12505 | C131 | direct (N × H) |
| 104. C131 | #12505 | direct (N × H) |
| 105. #2254 | C2×C131 | semidirect |
| 107. #2241 | C2×C131 | semidirect |
| 109. #1707 | C2×C131 | semidirect |
| 111. C8×C16 | C2×C131 | semidirect |
| 172. C16 | SD16×C131 | semidirect |
| 189. C8 | SD32×C131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2254×C131 | 2 |
| #2248×C131 | 2 |
| #2241×C131 | 2 |
| #2240×C131 | 2 |
| #1707×C131 | 2 |
| #1706×C131 | 2 |
| C8×C16×C131 | 2 |
| #12505 | 131 |