Finite Group DatabasebetaFinite Group DatabasebetaOrder 33536.
578 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 98 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 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C131 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C131 ◁ C2×C42×C131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #3214×C131 | C2 | semidirect |
| 2. #3213×C131 | C2 | semidirect |
| 3. #3153×C131 | C2 | semidirect |
| 4. #1496×C131 | C2 | semidirect |
| 5. #1484×C131 | C2 | semidirect |
| 6. #1469×C131 | C2 | semidirect |
| 7. #1291×C131 | C2 | semidirect |
| 212. #10120 | C131 | direct (N × H) |
| 213. C131 | #10120 | direct (N × H) |
| 214. #3214 | C2×C131 | semidirect |
| 215. #3213 | C2×C131 | semidirect |
| 216. #3153 | C2×C131 | semidirect |
| 217. #1496 | C2×C131 | semidirect |
| 218. #1484 | C2×C131 | semidirect |
| 219. #1469 | C2×C131 | semidirect |
| 220. #1291 | C2×C131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3214×C131 | 2 |
| #3213×C131 | 2 |
| #3153×C131 | 2 |
| #1496×C131 | 2 |
| #1484×C131 | 2 |
| #1469×C131 | 2 |
| #1291×C131 | 2 |
| #10120 | 131 |