Finite Group DatabasebetaFinite Group DatabasebetaOrder 35584.
426 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C139 | #1595 |
| commutator, Frattini, cosocle | C2×M16 | C23×C139 |
| LCS | G ▷ C2×M16 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C139 ◁ C2×C4×C139 ◁ C2×M16×C139 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #3197×C139 | C2 | semidirect |
| 2. #2191×C139 | C2 | semidirect |
| 3. #2190×C139 | C2 | semidirect |
| 4. #2010×C139 | C2 | semidirect |
| 5. #1340×C139 | C2 | semidirect |
| 6. #1339×C139 | C2 | semidirect |
| 7. #1320×C139 | C2 | semidirect |
| 34. C2×Q16×C139 | D4 | semidirect |
| 36. C2×D8×C139 | D4 | semidirect |
| 61. #106×C139 | D4 | semidirect |
| 62. #106×C139 | D4 | semidirect |
| 194. #12116 | C139 | direct (N × H) |
| 195. C139 | #12116 | direct (N × H) |
| 196. #3197 | C2×C139 | semidirect |
| 197. #2191 | C2×C139 | semidirect |
| 198. #2190 | C2×C139 | semidirect |
| 199. #2010 | C2×C139 | semidirect |
| 200. #1340 | C2×C139 | semidirect |
| 201. #1339 | C2×C139 | semidirect |
| 202. #1320 | C2×C139 | semidirect |
| 229. C2×Q16 | D4×C139 | semidirect |
| 231. C2×D8 | D4×C139 | semidirect |
| 256. #106 | D4×C139 | semidirect |
| 257. #106 | D4×C139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3197×C139 | 2 |
| #2191×C139 | 2 |
| #2190×C139 | 2 |
| #2010×C139 | 2 |
| #1340×C139 | 2 |
| #1339×C139 | 2 |
| #1320×C139 | 2 |
| #12116 | 139 |