Finite Group DatabasebetaFinite Group DatabasebetaOrder 35584.
348 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 78 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 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C139 |
| prime radical | #3191×C139 | C2 |
| LCS | G ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C139 ◁ C22×C4×C139 ◁ C2×C22⋊C8×C139 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #2235×C139 | C2 | semidirect |
| 3. #2232×C139 | C2 | semidirect |
| 4. #2075×C139 | C2 | semidirect |
| 5. #1348×C139 | C2 | semidirect |
| 6. #1347×C139 | C2 | semidirect |
| 7. #1314×C139 | C2 | semidirect |
| 168. #12280 | C139 | direct (N × H) |
| 169. C139 | #12280 | direct (N × H) |
| 171. #2235 | C2×C139 | semidirect |
| 172. #2232 | C2×C139 | semidirect |
| 173. #2075 | C2×C139 | semidirect |
| 174. #1348 | C2×C139 | semidirect |
| 175. #1347 | C2×C139 | semidirect |
| 176. #1314 | C2×C139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3191×C139 | 2 |
| #2235×C139 | 2 |
| #2232×C139 | 2 |
| #2075×C139 | 2 |
| #1348×C139 | 2 |
| #1347×C139 | 2 |
| #1314×C139 | 2 |
| #12280 | 139 |