Finite Group DatabasebetaFinite Group DatabasebetaOrder 35584.
680 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 118 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×C139 | B(4,𝔽2) |
| commutator | C2×Q8 | C22×C4×C139 |
| Frattini, cosocle | C22×Q8 | C23×C139 |
| prime radical | C2×#454×C139 | C2 |
| LCS | G ▷ C2×Q8 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C139 ◁ C23×C139 ◁ C22×Q8×C139 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #2379×C139 | C2 | semidirect |
| 3. C2×#355×C139 | C2 | semidirect |
| 4. #1793×C139 | C2 | semidirect |
| 5. #1394×C139 | C2 | semidirect |
| 10. #454×C139 | C4 | semidirect |
| 25. 2−1+4×C139 | C2×C4 | semidirect |
| 57. #101×C139 | C2×C4 | semidirect |
| 192. #13055 | C139 | direct (N × H) |
| 193. C139 | #13055 | direct (N × H) |
| 195. #2379 | C2×C139 | semidirect |
| 196. C2×#355 | C2×C139 | semidirect |
| 197. #1793 | C2×C139 | semidirect |
| 198. #1394 | C2×C139 | semidirect |
| 203. #454 | C4×C139 | semidirect |
| 218. 2−1+4 | C2×C4×C139 | semidirect |
| 250. #101 | C2×C4×C139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#454×C139 | 2 |
| #2379×C139 | 2 |
| C2×#355×C139 | 2 |
| #1793×C139 | 2 |
| #1394×C139 | 2 |
| #13055 | 139 |