Finite Group DatabasebetaFinite Group DatabasebetaOrder 33536.
1112 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 1112 conjugacy classes of subgroups — too many to draw. Only its 218 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C131 | B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×Q8 | C24×C131 |
| socle | C2×C131 | C2×B(4,𝔽2) |
| LCS | G ▷ C2×Q8 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C131 ◁ C2×C4×C131 ◁ C2×#41×C131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #3529×C131 | C2 | semidirect |
| 2. #3018×C131 | C2 | semidirect |
| 3. #2203×C131 | C2 | semidirect |
| 4. #2202×C131 | C2 | semidirect |
| 5. #2132×C131 | C2 | semidirect |
| 6. #585×C131 | C22 | semidirect |
| 8. #563×C131 | C22 | semidirect |
| 10. H(3,𝔽4)×C131 | C22 | semidirect |
| 15. #456×C131 | C22 | semidirect |
| 20. #413×C131 | C22 | semidirect |
| 21. #356×C131 | C22 | semidirect |
| 22. #355×C131 | C22 | semidirect |
| 168. #33564 | C131 | direct (N × H) |
| 169. C131 | #33564 | direct (N × H) |
| 170. #3529 | C2×C131 | semidirect |
| 171. #3018 | C2×C131 | semidirect |
| 172. #2203 | C2×C131 | semidirect |
| 173. #2202 | C2×C131 | semidirect |
| 174. #2132 | C2×C131 | semidirect |
| 175. #585 | C22×C131 | semidirect |
| 177. #563 | C22×C131 | semidirect |
| 179. H(3,𝔽4) | C22×C131 | semidirect |
| 184. #456 | C22×C131 | semidirect |
| 189. #413 | C22×C131 | semidirect |
| 190. #356 | C22×C131 | semidirect |
| 191. #355 | C22×C131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3529×C131 | 2 |
| #3018×C131 | 2 |
| #2203×C131 | 2 |
| #2202×C131 | 2 |
| #2132×C131 | 2 |
| #33564 | 131 |