Finite Group DatabasebetaFinite Group DatabasebetaOrder 35584.
446 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 446 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 | C23×C139 | #120 |
| commutator, Frattini, cosocle | C2×C42 | C23×C139 |
| prime radical | C22×D4×C139 | D4 |
| LCS | G ▷ C2×C42 ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C139 ◁ C2×C42×C139 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #2083×C139 | C2 | semidirect |
| 4. #2072×C139 | C2 | semidirect |
| 5. #1272×C139 | C2 | semidirect |
| 6. #1271×C139 | C2 | semidirect |
| 194. #7789 | C139 | direct (N × H) |
| 195. C139 | #7789 | direct (N × H) |
| 198. #2083 | C2×C139 | semidirect |
| 199. #2072 | C2×C139 | semidirect |
| 200. #1272 | C2×C139 | semidirect |
| 201. #1271 | C2×C139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2732×C139 | 2 |
| #2093×C139 | 2 |
| #2083×C139 | 2 |
| #2072×C139 | 2 |
| #1272×C139 | 2 |
| #1271×C139 | 2 |
| #1270×C139 | 2 |
| #7789 | 139 |