Finite Group DatabasebetaFinite Group DatabasebetaOrder 38144.
380 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 380 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×C149 | #394 |
| commutator, Frattini, cosocle | C2×C42 | C23×C149 |
| prime radical | C22×D4×C149 | D4 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C149 ◁ C2×C42×C149 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #1569×C149 | C2 | semidirect |
| 4. #1559×C149 | C2 | semidirect |
| 6. #1526×C149 | C2 | semidirect |
| 7. #1291×C149 | C2 | semidirect |
| 180. #10498 | C149 | direct (N × H) |
| 181. C149 | #10498 | direct (N × H) |
| 184. #1569 | C2×C149 | semidirect |
| 185. #1559 | C2×C149 | semidirect |
| 187. #1526 | C2×C149 | semidirect |
| 188. #1291 | C2×C149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3215×C149 | 2 |
| #1967×C149 | 2 |
| #1569×C149 | 2 |
| #1559×C149 | 2 |
| #1527×C149 | 2 |
| #1526×C149 | 2 |
| #1291×C149 | 2 |
| #10498 | 149 |