Finite Group DatabasebetaFinite Group DatabasebetaOrder 35584.
470 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 102 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 | C2×#99 |
| commutator | C22×C4 | C22×C4×C139 |
| Frattini, cosocle | C2×C4⋊C4 | C23×C139 |
| prime radical | #392×C139 | C4 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C139 ◁ C22×C4×C139 ◁ C2×#117×C139 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #1742×C139 | C2 | semidirect |
| 3. #1464×C139 | C2 | semidirect |
| 4. #1354×C139 | C2 | semidirect |
| 5. #1345×C139 | C2 | semidirect |
| 187. #11765 | C139 | direct (N × H) |
| 188. C139 | #11765 | direct (N × H) |
| 190. #1742 | C2×C139 | semidirect |
| 191. #1464 | C2×C139 | semidirect |
| 192. #1354 | C2×C139 | semidirect |
| 193. #1345 | C2×C139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2610×C139 | 2 |
| #1742×C139 | 2 |
| #1464×C139 | 2 |
| #1354×C139 | 2 |
| #1345×C139 | 2 |
| #11765 | 139 |