Order 35584.
1486 conjugacy classes of subgroups.
The subgroup lattice has 336 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C139 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C139 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24×C139 ◁ C22×C42×C139 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. #2056×C139 | C2 | direct (N × H) |
| 84. C22×C4×C139 | Q16 | semidirect |
| 136. C2×C4×C139 | C2×Q16 | semidirect |
| 161. C2×C139 | #2056 | direct (N × H) |
| 167. C2×#2056 | C139 | direct (N × H) |
| 168. C139 | C2×#2056 | direct (N × H) |
| 173. #2056 | C2×C139 | direct (N × H) |
| 252. C22×C4 | Q16×C139 | semidirect |
| 304. C2×C4 | C2×Q16×C139 | semidirect |
| 329. C2 | #2056×C139 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Q16×C139 | 2 |
| C22×C4⋊C8×C139 | 2 |
| C22×#103×C139 | 2 |
| C2×#391×C139 | 2 |
| #2056×C139 | 2 |
| C2×#340×C139 | 2 |
| C2×#2056 | 139 |