Finite Group DatabasebetaFinite Group DatabasebetaOrder 33536.
566 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 158 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 | C2×#102 |
| commutator | C2×C8 | C22×C4×C131 |
| Frattini, cosocle | C22×C8 | C23×C131 |
| prime radical | C2×#493×C131 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C131 ◁ C2×C42×C131 ◁ C2×C4×C8×C131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #2150×C131 | C2 | semidirect |
| 3. C2×#361×C131 | C2 | semidirect |
| 4. C4×#108×C131 | C2 | semidirect |
| 35. #108×C131 | D4 | semidirect |
| 95. C4×C131 | #361 | semidirect |
| 103. #13257 | C131 | direct (N × H) |
| 104. C131 | #13257 | direct (N × H) |
| 106. #2150 | C2×C131 | semidirect |
| 107. C2×#361 | C2×C131 | semidirect |
| 108. C4×#108 | C2×C131 | semidirect |
| 139. #108 | D4×C131 | semidirect |
| 199. C4 | #361×C131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#493×C131 | 2 |
| #2150×C131 | 2 |
| C2×#361×C131 | 2 |
| C4×#108×C131 | 2 |
| #13257 | 131 |