Finite Group DatabasebetaFinite Group DatabasebetaOrder 35584.
406 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 82 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 ◁ #436×C139 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #3273×C139 | C2 | semidirect |
| 2. #2250×C139 | C2 | semidirect |
| 3. #2206×C139 | C2 | semidirect |
| 4. #1687×C139 | C2 | semidirect |
| 5. #1360×C139 | C2 | semidirect |
| 6. #1333×C139 | C2 | semidirect |
| 7. #1330×C139 | C2 | semidirect |
| 14. #493×C139 | C22 | semidirect |
| 22. C4⋊C16×C139 | C22 | semidirect |
| 24. #346×C139 | C22 | semidirect |
| 25. #334×C139 | C22 | semidirect |
| 95. D8×C139 | D8 | semidirect |
| 179. #12324 | C139 | direct (N × H) |
| 180. C139 | #12324 | direct (N × H) |
| 181. #3273 | C2×C139 | semidirect |
| 182. #2250 | C2×C139 | semidirect |
| 183. #2206 | C2×C139 | semidirect |
| 184. #1687 | C2×C139 | semidirect |
| 185. #1360 | C2×C139 | semidirect |
| 186. #1333 | C2×C139 | semidirect |
| 187. #1330 | C2×C139 | semidirect |
| 194. #493 | C22×C139 | semidirect |
| 202. C4⋊C16 | C22×C139 | semidirect |
| 204. #346 | C22×C139 | semidirect |
| 205. #334 | C22×C139 | semidirect |
| 275. D8 | D8×C139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3273×C139 | 2 |
| #2250×C139 | 2 |
| #2206×C139 | 2 |
| #1687×C139 | 2 |
| #1360×C139 | 2 |
| #1333×C139 | 2 |
| #1330×C139 | 2 |
| #12324 | 139 |