Finite Group DatabasebetaFinite Group DatabasebetaOrder 35584.
884 conjugacy classes of subgroups; only the 206 normal subgroups are shown.
This group has 884 conjugacy classes of subgroups — too many to draw. Only its 206 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 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C139 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C139 ◁ #376×C139 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #2657×C139 | C2 | semidirect |
| 2. #2644×C139 | C2 | semidirect |
| 3. #2042×C139 | C2 | semidirect |
| 4. #2041×C139 | C2 | semidirect |
| 5. #2012×C139 | C2 | semidirect |
| 6. #2011×C139 | C2 | semidirect |
| 7. #1840×C139 | C2 | semidirect |
| 151. #32802 | C139 | direct (N × H) |
| 152. C139 | #32802 | direct (N × H) |
| 153. #2657 | C2×C139 | semidirect |
| 154. #2644 | C2×C139 | semidirect |
| 155. #2042 | C2×C139 | semidirect |
| 156. #2041 | C2×C139 | semidirect |
| 157. #2012 | C2×C139 | semidirect |
| 158. #2011 | C2×C139 | semidirect |
| 159. #1840 | C2×C139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2657×C139 | 2 |
| #2644×C139 | 2 |
| #2042×C139 | 2 |
| #2041×C139 | 2 |
| #2012×C139 | 2 |
| #2011×C139 | 2 |
| #1840×C139 | 2 |
| #32802 | 139 |