Finite Group DatabasebetaFinite Group DatabasebetaOrder 33536.
518 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 518 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 |
| prime radical | C22×D4×C131 | D4 |
| 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. #3166×C131 | C2 | semidirect |
| 4. #1534×C131 | C2 | semidirect |
| 5. #1515×C131 | C2 | semidirect |
| 7. #1288×C131 | C2 | semidirect |
| 194. #10023 | C131 | direct (N × H) |
| 195. C131 | #10023 | direct (N × H) |
| 196. #3166 | C2×C131 | semidirect |
| 199. #1534 | C2×C131 | semidirect |
| 200. #1515 | C2×C131 | semidirect |
| 202. #1288 | C2×C131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3166×C131 | 2 |
| #3110×C131 | 2 |
| #2633×C131 | 2 |
| #1534×C131 | 2 |
| #1515×C131 | 2 |
| #1490×C131 | 2 |
| #1288×C131 | 2 |
| #10023 | 131 |