Finite Group DatabasebetaFinite Group DatabasebetaOrder 35584.
458 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 90 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. D4×D8×C139 | C2 | semidirect |
| 2. #2246×C139 | C2 | semidirect |
| 3. #2206×C139 | C2 | semidirect |
| 4. #1667×C139 | C2 | semidirect |
| 5. #1361×C139 | C2 | semidirect |
| 6. #1331×C139 | C2 | semidirect |
| 7. D4⋊C16×C139 | C2 | semidirect |
| 13. #493×C139 | C22 | semidirect |
| 20. C4⋊C16×C139 | C22 | semidirect |
| 22. C4×C16×C139 | C22 | semidirect |
| 23. #335×C139 | C22 | semidirect |
| 82. D8×C139 | D8 | semidirect |
| 119. D4×C139 | D16 | semidirect |
| 162. #12316 | C139 | direct (N × H) |
| 163. C139 | #12316 | direct (N × H) |
| 164. D4×D8 | C2×C139 | semidirect |
| 165. #2246 | C2×C139 | semidirect |
| 166. #2206 | C2×C139 | semidirect |
| 167. #1667 | C2×C139 | semidirect |
| 168. #1361 | C2×C139 | semidirect |
| 169. #1331 | C2×C139 | semidirect |
| 170. D4⋊C16 | C2×C139 | semidirect |
| 176. #493 | C22×C139 | semidirect |
| 183. C4⋊C16 | C22×C139 | semidirect |
| 185. C4×C16 | C22×C139 | semidirect |
| 186. #335 | C22×C139 | semidirect |
| 245. D8 | D8×C139 | semidirect |
| 282. D4 | D16×C139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D8×C139 | 2 |
| #2246×C139 | 2 |
| #2206×C139 | 2 |
| #1667×C139 | 2 |
| #1361×C139 | 2 |
| #1331×C139 | 2 |
| D4⋊C16×C139 | 2 |
| #12316 | 139 |