Finite Group DatabasebetaFinite Group DatabasebetaOrder 35584.
346 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 86 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 | C4×C8 | C23×C139 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C139 ◁ C42×C139 ◁ C8×D4×C139 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #3334×C139 | C2 | semidirect |
| 2. #2240×C139 | C2 | semidirect |
| 3. #2206×C139 | C2 | semidirect |
| 4. #1667×C139 | C2 | semidirect |
| 5. #1364×C139 | C2 | semidirect |
| 6. #1331×C139 | C2 | semidirect |
| 7. D4⋊C16×C139 | C2 | semidirect |
| 102. D4×C139 | D16 | semidirect |
| 143. #12340 | C139 | direct (N × H) |
| 144. C139 | #12340 | direct (N × H) |
| 145. #3334 | C2×C139 | semidirect |
| 146. #2240 | C2×C139 | semidirect |
| 147. #2206 | C2×C139 | semidirect |
| 148. #1667 | C2×C139 | semidirect |
| 149. #1364 | C2×C139 | semidirect |
| 150. #1331 | C2×C139 | semidirect |
| 151. D4⋊C16 | C2×C139 | semidirect |
| 246. D4 | D16×C139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3334×C139 | 2 |
| #2240×C139 | 2 |
| #2206×C139 | 2 |
| #1667×C139 | 2 |
| #1364×C139 | 2 |
| #1331×C139 | 2 |
| D4⋊C16×C139 | 2 |
| #12340 | 139 |